Question

question 4 a flagpole is tilted at an angle of 7° from the vertical and toward the sun. it casts a shadow of 14.3 m when the angle of elevation of the sun is 32°. find the length of the flagpole. answer to the nearest tenth of a metre. > show answer the answer is: 9 8 11

Explanation:

Step1: Find the angle between the flag - pole and the ground

The flag - pole is tilted at an angle of $7^{\circ}$ from the vertical towards the sun. So the angle between the flag - pole and the ground is $\theta=90^{\circ}-7^{\circ}=83^{\circ}$. The angle of elevation of the sun is $\alpha = 32^{\circ}$, and the length of the shadow is $s = 14.3$ m.

Step2: Use the sine - rule in the triangle formed by the flag - pole, its shadow, and the line from the top of the flag - pole to the end of the shadow

Let the length of the flag - pole be $l$. In the triangle, the third angle $\beta=180^{\circ}-(83^{\circ}+32^{\circ})=65^{\circ}$. According to the sine - rule $\frac{l}{\sin\alpha}=\frac{s}{\sin\beta}$.

Step3: Solve for the length of the flag - pole

We know that $l=\frac{s\sin\alpha}{\sin\beta}$. Substitute $s = 14.3$ m, $\alpha = 32^{\circ}$, and $\beta=65^{\circ}$ into the formula. $\sin32^{\circ}\approx0.5299$ and $\sin65^{\circ}\approx0.9063$. Then $l=\frac{14.3\times0.5299}{0.9063}=\frac{7.57757}{0.9063}\approx8.4$ m.

Answer:

$8.4$ m