Question

A student draws a triangle with a 90° angle. They label one of the other angles as θ. The hypotenuse has a length of 10.7 cm. The adjacent side relative to angle θ has a length of 8.9 cm. Calculate the size of angle θ. Give your answer in degrees to the nearest integer.

Answer 1

To calculate the size of angle θ, we use the cosine trigonometric ratio. Cos(θ) = 8.9 cm / 10.7 cm and then θ = arccos(8.9 / 10.7). After calculating and rounding, the size of angle θ is approximately 34°.

Step-by-step explanation:

To calculate the size of angle θ in a right triangle where the hypotenuse is 10.7 cm and the adjacent side to θ is 8.9 cm, we can use the cosine trigonometric function. Remembering that the cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse, we have:

cos(θ) = adjacent side / hypotenuse = 8.9 cm / 10.7 cm

To find the angle θ, we take the inverse cosine (arccos) of the ratio:

θ = cos⁻¹(8.9 / 10.7)

Using a calculator, we find that:

θ ≈ cos⁻¹(0.8317757009)

θ ≈ 33.69°

Since the question asks for the nearest integer, we round θ to 34° to obtain our final answer.