The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then height of the temple is
45m
CE is the building = 30 m and AD is the temple By symmetry, BD = CE = 30 m, and DE = BC = y m Let AB = x m Also, ∠AED = 60° and ∠ACB = 30° In ∆ ADE,=>tan (∠AED)=AD/DE => tan60= √3=(x+30)/y => x+30=y√3 ------------(i) In ∆ABC,=>tan(∠ACB)=AB/BC =>tan30=1/√3=x/y =>y=x√3 Substituting it in equation (i), we get: => x + 30 = (x √3) × √3 = 3x =>3x-x=2x=30 => x=30/2=15 m ∴AD = AB + BD = 15 + 30 = 45 meters
Similar Questions
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
Which one of the following combinations of measurements can form the sides of a triangle?
If \( \frac{3}{(x+2)(x+1)} = \frac{a}{2x+1} + \frac{b}{x^2+1} \) be an identity, then the value of \( b \) is:
From the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is \( \sqrt{3} = 1.732 \):
The circular measure of the included angle formed by the hour hand and minute hand of a clock at 3 PM will be
If Sin 31° = x/y, the value of Sec 31° - Sin 59° is
A tower is 50 meters high. Its shadow is x meters shorter when the sun’s altitude is 45° than when it is 30°. The value of x in metres is
The value of (sec245° - cot245°) - (sin230° + sin260°) is
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
Important Questions from Trigonometry
(secθ + tanθ)/(secθ - tanθ) is equal to:
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
what is the principal value of \(\sin^{-1} \left( \sin \dfrac{2 \pi}{3} \right)\) ?
- \(\sqrt{2 + \sqrt{2 +\sqrt {2 + 2 \cos 8\theta}}}\) is equal to
