Question

A tree 15 meters high casts a 21.4 meter shadow. Find the angle of elevation of the sun.

Answer 1

So we can set up a right triangle in this situation with one of the legs being 21.4m and the height being 15m. Then we can use trigonometric formulas to find the angle of elevation of the sun.

Since we have the dimensions for the opposite and the adjacent sides, we can use the trigonometric function tangent to find the angle:

$tan(theta)=\frac{opposite}{adjacent}$

So let's plug this in:

$tan(theta)=\frac{15}{21.4}$

$theta=tan^{-1}(\frac{15}{21.4})$

$theta=1.18499$

However this is in radians - to convert to degrees, we must use the formula:

$Degrees=\frac{180}{\pi} *radians$

So then let's solve for degrees:

$Degrees=\frac{180}{\pi} *1.18499$

$Degrees=\frac{213.2982}{\pi}$

$Degrees=67.89$

So now we know that the angle of elevation is 67.89°.