We are given: - The angle between the two radii of a circle is 100°. Key property of tangents The tangents drawn at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii. Calculate the angRead more
We are given:
– The angle between the two radii of a circle is 100°.
Key property of tangents
The tangents drawn at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii.
Calculate the angle between the tangents
The sum of the angle between the radii and the angle between the tangents is 180° (since they form a quadrilateral with two right angles). Thus:
Angle between tangents = 180° – Angle between radii.
Substitute the given angle between the radii:
Angle between tangents = 180° – 100° = 80°.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
A circle can have two parallel tangents. These tangents will always be parallel to each other and lie on opposite sides of the circle, touching it at two distinct points. Explanation: - A tangent is a line that touches a circle at exactly one point. - For any given direction, there can be two tangenRead more
A circle can have two parallel tangents. These tangents will always be parallel to each other and lie on opposite sides of the circle, touching it at two distinct points.
Explanation:
– A tangent is a line that touches a circle at exactly one point.
– For any given direction, there can be two tangents to a circle that are parallel to each other, one on each side of the circle.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
We are given: Height of the girl = 1.5 m, Distance of the girl from the lamp-post = 3 m, Length of the shadow cast by the girl = 4.5 m. Use similar triangles The height of the lamp-post (H) and the total length of the shadow (distance from the base of the lamp-post to the end of the shadow) form a lRead more
We are given:
Height of the girl = 1.5 m,
Distance of the girl from the lamp-post = 3 m,
Length of the shadow cast by the girl = 4.5 m.
Use similar triangles
The height of the lamp-post (H) and the total length of the shadow (distance from the base of the lamp-post to the end of the shadow) form a larger triangle. The height of the girl and her shadow form a smaller, similar triangle.
From similar triangles:
(Height of lamp-post) / (Total shadow length) = (Height of girl) / (Length of girl’s shadow).
Substitute the values:
H / (3 + 4.5) = 1.5 / 4.5.
Simplify:
H / 7.5 = 1.5 / 4.5.
Solve for H
Simplify the ratio on the right-hand side:
1.5 / 4.5 = 1/3.
Thus:
H / 7.5 = 1/3.
Multiply through by 7.5:
H = 7.5 × (1/3) = 2.5 m.
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
We are given: Height of the first pole = 16 m, Height of the second pole = 10 m, The wire makes an angle of 30° with the horizontal. Find the vertical difference between the tops of the poles The vertical difference between the tops of the two poles is: 16 - 10 = 6 m. Step 2: Use the sine functionRead more
We are given:
Height of the first pole = 16 m,
Height of the second pole = 10 m,
The wire makes an angle of 30° with the horizontal.
Find the vertical difference between the tops of the poles
The vertical difference between the tops of the two poles is:
16 – 10 = 6 m.
Step 2: Use the sine function
The wire forms the hypotenuse of a right triangle, where:
The vertical difference (6 m) is the opposite side,
The angle between the wire and the horizontal is 30°.
Using the sine function:
sinθ = (Opposite side) / (Hypotenuse).
Substitute the values:
sin30° = 6 / l.
From trigonometric values, sin30° = 1/2:
1/2 = 6 / l.
Solve for l
Multiply through by l:
l × (1/2) = 6.
Simplify:
l = 6 × 2 = 12 m
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
Given: - Angle of elevation changes from 30° to 60° as we walk x meters towards the chimney. Using tangent for both angles: 1. tan30° = h / d ⇒ d = h√3. 2. tan60° = h / (d - x) ⇒ d - x = h / √3. Substitute d = h√3 into d - x = h / √3: h√3 - x = h / √3. Simplify: x = h√3 - h / √3 = (2h) / √3. Solve fRead more
Given:
– Angle of elevation changes from 30° to 60° as we walk x meters towards the chimney.
Using tangent for both angles:
1. tan30° = h / d ⇒ d = h√3.
2. tan60° = h / (d – x) ⇒ d – x = h / √3.
Substitute d = h√3 into d – x = h / √3:
h√3 – x = h / √3.
Simplify:
x = h√3 – h / √3 = (2h) / √3.
Solve for h:
h = (√3 / 2) x.
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
If the angle between the ratio of a circle is 100°, then the angle between the tangents at the end of these radii is
We are given: - The angle between the two radii of a circle is 100°. Key property of tangents The tangents drawn at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii. Calculate the angRead more
We are given:
– The angle between the two radii of a circle is 100°.
Key property of tangents
The tangents drawn at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii.
Calculate the angle between the tangents
The sum of the angle between the radii and the angle between the tangents is 180° (since they form a quadrilateral with two right angles). Thus:
Angle between tangents = 180° – Angle between radii.
Substitute the given angle between the radii:
Angle between tangents = 180° – 100° = 80°.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
How many parallel tangents can a circle have?
A circle can have two parallel tangents. These tangents will always be parallel to each other and lie on opposite sides of the circle, touching it at two distinct points. Explanation: - A tangent is a line that touches a circle at exactly one point. - For any given direction, there can be two tangenRead more
A circle can have two parallel tangents. These tangents will always be parallel to each other and lie on opposite sides of the circle, touching it at two distinct points.
Explanation:
– A tangent is a line that touches a circle at exactly one point.
– For any given direction, there can be two tangents to a circle that are parallel to each other, one on each side of the circle.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If a 1.5 m tall girl stands at a distance of 3m from a lamp-post and casts a shadow of length 4.5m on the ground, then the height of the lamp-post is
We are given: Height of the girl = 1.5 m, Distance of the girl from the lamp-post = 3 m, Length of the shadow cast by the girl = 4.5 m. Use similar triangles The height of the lamp-post (H) and the total length of the shadow (distance from the base of the lamp-post to the end of the shadow) form a lRead more
We are given:
Height of the girl = 1.5 m,
Distance of the girl from the lamp-post = 3 m,
Length of the shadow cast by the girl = 4.5 m.
Use similar triangles
The height of the lamp-post (H) and the total length of the shadow (distance from the base of the lamp-post to the end of the shadow) form a larger triangle. The height of the girl and her shadow form a smaller, similar triangle.
From similar triangles:
(Height of lamp-post) / (Total shadow length) = (Height of girl) / (Length of girl’s shadow).
Substitute the values:
H / (3 + 4.5) = 1.5 / 4.5.
Simplify:
H / 7.5 = 1.5 / 4.5.
Solve for H
Simplify the ratio on the right-hand side:
1.5 / 4.5 = 1/3.
Thus:
H / 7.5 = 1/3.
Multiply through by 7.5:
H = 7.5 × (1/3) = 2.5 m.
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
The tops of two poles of height 16m and 10m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =
We are given: Height of the first pole = 16 m, Height of the second pole = 10 m, The wire makes an angle of 30° with the horizontal. Find the vertical difference between the tops of the poles The vertical difference between the tops of the two poles is: 16 - 10 = 6 m. Step 2: Use the sine functionRead more
We are given:
Height of the first pole = 16 m,
Height of the second pole = 10 m,
The wire makes an angle of 30° with the horizontal.
Find the vertical difference between the tops of the poles
The vertical difference between the tops of the two poles is:
16 – 10 = 6 m.
Step 2: Use the sine function
The wire forms the hypotenuse of a right triangle, where:
The vertical difference (6 m) is the opposite side,
The angle between the wire and the horizontal is 30°.
Using the sine function:
sinθ = (Opposite side) / (Hypotenuse).
Substitute the values:
sin30° = 6 / l.
From trigonometric values, sin30° = 1/2:
1/2 = 6 / l.
Solve for l
Multiply through by l:
l × (1/2) = 6.
Simplify:
l = 6 × 2 = 12 m
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
It is found that on walking x meters towards a chimney in a horizontal line through its base, the elevation of its top changes from 30° to 60°. The height of the chimney is
Given: - Angle of elevation changes from 30° to 60° as we walk x meters towards the chimney. Using tangent for both angles: 1. tan30° = h / d ⇒ d = h√3. 2. tan60° = h / (d - x) ⇒ d - x = h / √3. Substitute d = h√3 into d - x = h / √3: h√3 - x = h / √3. Simplify: x = h√3 - h / √3 = (2h) / √3. Solve fRead more
Given:
– Angle of elevation changes from 30° to 60° as we walk x meters towards the chimney.
Using tangent for both angles:
1. tan30° = h / d ⇒ d = h√3.
2. tan60° = h / (d – x) ⇒ d – x = h / √3.
Substitute d = h√3 into d – x = h / √3:
h√3 – x = h / √3.
Simplify:
x = h√3 – h / √3 = (2h) / √3.
Solve for h:
h = (√3 / 2) x.
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/