Question

estimation a ramp is being built to a building to help with deliveries. the angle that the bottom of the ramp makes with the ground is 34.5°. estimate the measure of the other acute angle. find the exact measure of the other acute angle. which of the following is a good estimate for the measure of the other acute angle? a. 65 b. 50° c. 60°

Explanation:

Step1: Recall the property of right - angled triangles

In a right - angled triangle, the sum of the two acute angles is \(90^{\circ}\). Let the unknown acute angle be \(x\). Then \(x + 34.5^{\circ}=90^{\circ}\).

Step2: Estimate the value

We know that \(34.5^{\circ}\approx35^{\circ}\). Using the formula \(x = 90^{\circ}-\text{known acute angle}\), when the known acute angle is approximately \(35^{\circ}\), then \(x\approx90^{\circ}- 35^{\circ}=55^{\circ}\). Among the given options, \(60^{\circ}\) is the closest estimate.

Step3: Calculate the exact value

Using the formula \(x = 90^{\circ}-34.5^{\circ}\), we have \(x=(90 - 34.5)^{\circ}=55.5^{\circ}\)

Answer:

C. \(60^{\circ}\) (estimate), \(55.5^{\circ}\) (exact)