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 \( \sqrt{3} = 1.732 \):
54.64 m
Let the height of the building be AB = 20 m. Let the height of the tower be CD = h m. The angle of elevation of the top of the tower from the top of the building is 60°, so ∠EAB = 60°. The angle of depression of the foot of the tower from the top of the building is 45°, so ∠DAB = 45°. In right-angled triangle ABE, we have:
\(\tan 60° = \frac{BE}{AB}\)
\(\sqrt{3} = \frac{BE}{20}\)
\(BE = 20\sqrt{3}\)
In right-angled triangle ABD, we have:
\(\tan 45° = \frac{AB}{BD}\)
\(1 = \frac{20}{BD}\)
\(BD = 20\)
Since BD = AE = 20 m, the height of the tower is given by:
\(CD = CE + ED = CE + AB\)
\(h = 20\sqrt{3} + 20\)
\(h = 20(\sqrt{3} + 1)\)
\(h = 20(1.732 + 1) = 20(2.732) = 54.64 m\)
Therefore, the height of the tower is 54.64 m.
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
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
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:
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
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
what is the principal value of \(\sin^{-1} \left( \sin \dfrac{2 \pi}{3} \right)\) ?
