Question

1. the eiffel tower in paris casts a shadow 150 meters long when the angle of elevation of the sun is 63°26. find the height of the tower.

Explanation:

Step1: Recall tangent formula

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ in a right - triangle. Here, $\theta = 63^{\circ}26'$, the adjacent side to the angle of elevation is the length of the shadow ($x = 150$ m) and the opposite side is the height of the tower ($h$).

Step2: Convert the angle to decimal degrees

$26'=\frac{26}{60}\approx0.433^{\circ}$, so $63^{\circ}26'\approx63.433^{\circ}$.

Step3: Calculate the height

Since $\tan\theta=\frac{h}{x}$, then $h = x\tan\theta$. Substitute $x = 150$ m and $\theta\approx63.433^{\circ}$ into the formula. $\tan(63.433^{\circ})\approx2$. So $h=150\times\tan(63.433^{\circ})\approx150\times2 = 300$ m.

Answer:

300 m