91Ó°ÊÓ

The perimeter of an equilateral triangle is 45 centimeters. Find the length of an altitude of the triangle.

Use \(\triangle P Q R\) with right angle \(R\) to find \(\sin P, \cos P, \tan P\) \(\sin Q, \cos Q,\) and tan \(Q .\) Express each ratio as a fraction, and as a decimal to the nearest hundredth. $$p=2 \sqrt{3}, q=\sqrt{15}, \text { and } r=3 \sqrt{3}$$

Determine whether \(\triangle Q R S\) is a right triangle for the given vertices. Explain. $$Q(-4,6), R(2,11), S(4,-1)$$

Determine whether \(\triangle Q R S\) is a right triangle for the given vertices. Explain. $$Q(-9,-2), R(-4,-4), S(-6,-9)$$

Use a calculator to find each value. Round to the nearest ten- thousandth.$$\sin 6^{\circ}$$

The length of a diagonal of a square is \(22 \sqrt{2}\) millimeters. Find the perimeter of the square.

Determine whether each set of numbers can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean triple. $$8,15,17$$

The altitude of an equilateral triangle is 7.4 meters long. Find the perimeter of the triangle.

MEDICINE For Exercises 19-21, use the following information. A doctor is using a treadmill to assess the strength of a patient's heart. At the beginning of the exam, the 48 -inch long treadmill is set at an incline of \(10^{\circ} .\) How far off the horizontal is the raised end of the treadmill at the beginning of the exam?

Use a calculator to find each value. Round to the nearest ten-thousandth. $$\tan 42.8^{\circ}$$