A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 30 ° angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is 6 m . Find the height of the tree before falling down.

Let A C be the original tree and A ' B be the broken part which makes an angle of 30 o with the ground. In ∆ A ' B C , tan 30 o = B C A ' C ⇒ 1 3 = B C 6 ⇒ B C = 6 3 = 6 3 3 = 2 3 Again, cos 30 o = A ' C A ' B ⇒ 3 2 = 6 A ' B ⇒ A ' B = 12 3 = 12 3 3 = 4 3 The height of the tree = A ' B + B C = 2 3 + 4 3 = 6 3 m Hence, the height of the tree is 6 3 m .

Rehman observed the top of a temple at an angle of elevation of 30 ° , when the observation point is 24 m . away from the foot of the temple. Find the height of the temple.

Let A B represents the height of the temple, O represents the Rehman position of point of observation. O B is the distance between the observation point and the foot of the temple. So, ∠ A O B = 30 ° , and O B = 24 m According to the given data, Here ∆ A O B forms a right angle triangle. Now, we need to find the opposite side of ∠ A O B in the triangle ∆ O A B . So, we need to consider the trigonometric ratio “tangent” to solve the problem tan θ = Opposite side Adjacent side tan 30 ° = A B O B ⇒ 1 3 = A B 24 ⇒ A B = 24 3 = 24 3 3 = 8 3 Hence, the height of the temple is 8 3 m .

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 31

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IMPORTANT

Earn 100

From the top of the building the angle of elevation of the top of the cell tower is $60 °$ and the angle of depression to its foot is $45 °$ , if the distance of the building from the tower is $30$ meters, which of the following represent the correct diagram for solving the question?

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Important Questions on Applications of Trigonometry

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 32

From the top of a tower of

h m

height, Anusha observes the angles of depression of two points

X

and

Y

on the same side of tower on the ground to be

α

and

β

. Identify the suitable figure for the given information.

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 33

The ratio of the length of a pole and its shadow is

1 : \sqrt{3}

. The angle of elevation of the sun is:

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 34

If the ratio of height of a tower and the length of its shadow on the ground is

\sqrt{3} : 1

, then the angle of elevation of the sun is

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 35

The length of the string of a kite flying at

100 m

above the ground with the elevation of

60 °

is

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 36

The length of the shadow of a

20 m

tall pole on the ground when the sun's elevation is

45 °

is

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 37

If sun's elevation is

60 °

, then a pole of height

6 m

will cast a shadow of length.

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 38

You are observing top of your school building at an angle of elevation $α$ from a point which is at $d$ meter distance from the foot of the building. Which trigonometric ratio would you like to consider, to find the height of the building?

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 12 - Applications of Trigonometry>Exercise>Q 39

A ladder of length