Worked exercise — The sun's angle from the shadow

Problem

A person $1{,}62\;\text{m}$ tall casts a shadow on the ground $0{,}5\;\text{m}$ long. What is the elevation angle of the sun above the horizon?

Solution

Step 1 — Identifying the right triangle. The sunlight, the body, and the shadow form a right triangle, with angle $\alpha$ between the sun’s rays and the ground. The person is the side opposite $\alpha$ ($o = 1{,}62\;\text{m}$), the shadow is the adjacent side ($a = 0{,}5\;\text{m}$).

Step 2 — Applying the tangent. Since $\tan\alpha = o/a$:

$\tan\alpha = \frac{o}{a} = \frac{1{,}62}{0{,}5} = 3{,}24$

Step 3 — Finding the angle. Inverting with the arctangent:

$\ev{\alpha = \arctan 3{,}24 \approx 72{,}8^\circ}$

Links

Topics: Physical quantities and measurement Skills: Use of trigonometry