From the top of a tower, the angle of depression of the top of a 10 m high building is 60°. If the distance between the tower and the building is 50√3 m, find the height of the tower.
160 m
The angle of depression is 60°. Therefore, we can use the tangent formula in right-angled triangles: \[ \tan(60^\circ) = \frac{\text{height of tower - height of building}}{\text{distance}} \] Substituting the known values: \[ \tan(60^\circ) = \frac{h - 10}{50\sqrt{3}} \] Using \(\tan(60^\circ) = \sqrt{3}\): \[ \sqrt{3} = \frac{h - 10}{50\sqrt{3}} \quad \Rightarrow \quad h - 10 = 150 \quad \Rightarrow \quad h = 160 \]
Similar Questions
- If $\sin(x) = 0.6$ and $x \in (0, \pi/2)$, find $\sin(2x) + \cos(2x)$.
- If $\cos A = 1 - 2\sin^2A$, then what is the value of $\cos 2A$?
- If $\sin(3x + 10^{\circ}) = \cos(2x - 5^{\circ})$, find x.
- If $\sin(A) = \cos(B), \cos(A) = \sin(C)$, and $A + B + C = 90^\circ$, then what is the value of angle A?
- A triangle has sides 8 cm and 10 cm, and the angle between them is $120^\circ$. What is its area?
- If $\sin A = 0.6$ and $\cos A = 0.8$, what is $\tan A$?
- If $\sin A = 0.6$, what is the value of $\tan A$ ?
- If $\sec A + \tan A = p$, then what is $\sec A$ in terms of p?
- Which of the following is true for all acute angles A?
- If $\tan x = \cot(3x - 30^\circ)$, find $x$.
Important Questions from Trigonometry
The value of 5 sin 14° sec 76° + 3 cot 15° cot 75° + 2 tan 45° is:
If two complimentary angles are in the ratio of 4 : 5, find the greater angle.
If \(\frac{\sin\spaceθ \space+\space \cos\spaceθ} {\sin \spaceθ \space-\space \cos \spaceθ} = \frac{\sqrt3 \space-\space 1}{\sqrt3 \space+\space 1} \) , then the angle θ is
If tan α = 1/2, tan β = 1/3, then find α + β.
Simplify: sin (A + B) sin (A – B)
