Questions: The front of the tent shown in the diagram below is an isosceles triangle. Calculate the size of angle θ. Give your answer to the nearest integer.

Solution Steps

The base of the isosceles triangle is 2.4 m. Since the triangle is isosceles, the perpendicular from the vertex bisects the base. Therefore, the adjacent side has length 2.4 m / 2 = 1.2 m.

We are given the hypotenuse (3.1 m) and the adjacent side (1.2 m). We can use the cosine function to find the angle $\theta$.

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

$\cos(\theta) = \frac{1.2}{3.1}$

$\cos(\theta) \approx 0.3871$

$\theta = \cos^{-1}(0.3871)$

$\theta \approx 67.23^\circ$

Rounding to the nearest integer, we get $\theta \approx 67^\circ$.

Final Answer