Question

1. an isosceles triangle has the equal side lengths of 16 cm and a base of 12 cm. calculate the size of angle ( a ), the base angle, to one decimal place.

Explanation:

Step1: Split the triangle

Draw a perpendicular from the top vertex to the base, splitting the isosceles triangle into two right - angled triangles. The base of each right - angled triangle is $\frac{12}{2}=6$ cm, and the hypotenuse is 16 cm.

Step2: Use cosine formula

In a right - angled triangle, $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to angle $A$ is 6 cm and the hypotenuse is 16 cm. So $\cos A = \frac{6}{16}=\frac{3}{8}$.

Step3: Calculate angle A

To find angle $A$, we use the inverse cosine function: $A=\cos^{- 1}(\frac{3}{8})$. Using a calculator, $\cos^{-1}(\frac{3}{8})\approx67.9796^{\circ}$. Rounding to one decimal place, we get $A\approx68.0^{\circ}$.

Answer:

$68.0^{\circ}$