2. Trigonometric Functions on Right Triangles

Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. WNBA Scorer Women's National Basketball Association player Breanna Stewart of the Seattle Storm was the WNBA's top scorer for the 2018 regular season, with 742 points. Is it appropriate to consider this number between 741.5 and 742.5? Why or why not? (Data from www.wnba.com)

Given a right triangle with one leg of length $5$ and hypotenuse of length $13$, what is the approximate length of the other leg?

Solve each problem. See Examples 1–4. Diameter of the Sun To determine the diameter of the sun, an astronomer might sight with a transit (a device used by surveyors for measuring angles) first to one edge of the sun and then to the other, estimating that the included angle equals 32'. Assuming that the distance d from Earth to the sun is 92,919,800 mi, approximate the diameter of the sun.

In a right triangle, one leg has length $6$ and the hypotenuse has length $10$. Find the length of the other leg $x$ in simplest radical form with a rational denominator.

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. b = 2, c = 7

In a right triangle, one leg has length $6$, the hypotenuse has length $10$, and $x$ is the length of the other leg. What is the value of $x$?

In Exercises 54–57, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 22.3°, c = 10

Solve each problem. See Examples 3 and 4. Angle of Depression of a Light A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit, as shown in the figure. Find the angle of depression of the light to the nearest minute.

A right triangle has a base of $68$ units and the angle opposite the height is $15°$. What is the height of the triangle?

Triangle xyz was transformed by a dilation with center O and scale factor $3$. If the original length of side xy was $1.5$ units, what is the length of side xy after the transformation?

Triangle QRS is a right triangle with angle Q equal to $90°$ and angle R equal to $35°$. What is the measure of the obtuse angle in triangle QRS?

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. B = 51.7°, a = 28.1 ft

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. B = 16.8°, b = 30.5

Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. Mt. Everest When Mt. Everest was first surveyed, the surveyors obtained a height of 29,000 ft to the nearest foot. State the range represented by this number. (The surveyors thought no one would believe a measurement of 29,000 ft, so they reported it as 29,002.) (Data from Dunham, W., The Mathematical Universe, John Wiley and Sons.)

In a right triangle $FGH$, if the length of $FH$ is $18$ units and angle $G$ is $30°$, what is the length of side $FG$ opposite angle $H$?