When solving a right triangle, we will use the sine, cosine, and tangent functions, rather than their reciprocals.

Solve the right triangle shown below, rounding lengths to two decimal places.

Which trig function will we use? We will use the tangent function.

Which trig function will we use? We will use the cosine function.

From a point on level ground 125 feet from the base of a tower, the angle of elevation is 57.2°. Approximate the height of the tower to the nearest foot. Let’s first draw a sketch of this figure. We want a triangle. It doesn’t need to be drawn to scale. Then place the given information. Line of sight Height of tower Where is the angle of elevation?

Which trig function will we use to find the height of the tower? Line of sight Height of tower tangent The height of the tower is approximately 194 ft.

A kite flies at a height of 30 feet when 65 feet of string is out. If the string is in a straight line, find the angle that it makes with the ground. Round to the nearest tenth of a degree. String = 65 ft. Height of kite = 30 ft. Which trig function will we use to find the angle measure? sine The string makes an angle of approximately 27.5° with the ground.

You are taking your first hot-air balloon ride. Your friend is standing on level ground, 100 feet away from your point of launch, making a video of the terrified look on your rapidly ascending face. How rapidly? At one instant, the angle of elevation from the video camera to your face is 31.7°. One minute later, the angle of elevation is 76.2°. How far did you travel, to the nearest tenth of a foot, during that minute?

Each bearing has three parts: a letter (N or S), the measure of an acute angle, and a letter (E or W). Here’s how we write a bearing: If the acute angle is measured from the north side of the north-south line, then we write N first. See Figure (a). If the acute angle is measured from the south side of the north-south line, then we write S first. See Figure (c). Second, we write the measure of the acute angle. If the acute angle is measured on the east side of the north-south line, then we write E last. See Figure (a). If the acute angle is measured on the west side of the north-south line, then we write W last. See Figure (b).

A boat leaves the entrance to a harbor and travels 25 miles on a bearing of N 42° E. The figure below shows that the captain then turns the boat 90° clockwise and travels 18 miles on a bearing of S 48° E. At that time: How far is the boat, to the nearest tenth of a mile, from the harbor entrance? The boat is approximately 30.8 miles from the harbor entrance.

What is the bearing, to the nearest tenth of a degree, of the boat from the harbor entrance?