Example 1: Two friends, Rakesh and Vishal started climbing a pyramid-shaped hill. Rakesh climbs 315 m and finds that the angle of depression is 72.3 degrees from his starting point. How high is he from the ground?
Solution: Let m is the height above the ground.
To find: Value of m
To solve m, use the sine ratio.
Sin 72.3° = m/315
0.953 = m/315
m= 315 x 0.953
m=300.195 mtr
The man is 300.195 mtr above the ground.
Example 2: A man is observing a pole of height 55 foot. According to his measurement, pole cast a 23 feet long shadow. Can you help him to know the angle of elevation of the sun from the tip of shadow?
Solution:
Let x be the angle of elevation of the sun, then
tan x = 55/23 = 2.391
x = tan-1(2.391)
or x = 67.30 degrees
Trigonometry Questions
Practise these questions given here to get a deep knowledge of Trigonometry. Use the formulas and table given in this article wherever necessary.
Q.1: In △ABC, right-angled at B, AB=22 cm and BC=17 cm. Find:
(a) sin A Cos B
(b) tan A tan B
Q.2: If 12cot θ= 15, then find sec θ.
Q.3: In Δ PQR, right-angled at Q, PR + QR = 30 cm and PQ = 10 cm. Determine the values of sin P, cos P and tan P.
Q.4: If sec 4θ = cosec (θ- 300), where 4θ is an acute angle, find the value of A.
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