사인법칙과 코사인법칙

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$a=5,c=6,\beta =\,35^\circ$

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$b=11,c=8,\alpha =28^\circ$

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$a=32,b=24,\gamma =75^\circ$

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$a=7.2,b=4.5,\gamma =43^\circ$

In order to estimate the height of a building, two students stand at a certain distance from the building at street level. From this point, they find the angle of elevation from the street to the top of the building to be 39°. They then move 300 feet closer to the building and find the angle of elevation to be 50°. Assuming that the street is level, estimate the height of the building to the nearest foot.

In order to estimate the height of a building, two students stand at a certain distance from the building at street level. From this point, they find the angle of elevation from the street to the top of the building to be 35°. They then move 250 feet closer to the building and find the angle of elevation to be 53°. Assuming that the street is level, estimate the height of the building to the nearest foot.

Points $A$ and $B$ are on opposite sides of a lake. Point $C$ is 97 meters from $A.$ The measure of angle $BAC$ is determined to be 101°, and the measure of angle $ACB$ is determined to be 53°. What is the distance from $A$ to $B,$ rounded to the nearest whole meter?

Two search teams spot a stranded climber on a mountain. The first search team is 0.5 miles from the second search team, and both teams are at an altitude of 1 mile. The angle of elevation from the first search team to the stranded climber is 15°. The angle of elevation from the second search team to the climber is 22°. What is the altitude of the climber? Round to the nearest tenth of a mile.

A street light is mounted on a pole. A 6-foot-tall man is standing on the street a short distance from the pole, casting a shadow. The angle of elevation from the tip of the man’s shadow to the top of his head of 28°. A 6-foot-tall woman is standing on the same street on the opposite side of the pole from the man. The angle of elevation from the tip of her shadow to the top of her head is 28°. If the man and woman are 20 feet apart, how far is the street light from the tip of the shadow of each person? Round the distance to the nearest tenth of a foot.

Two streets meet at an 80° angle. At the corner, a park is being built in the shape of a triangle. Find the area of the park if, along one road, the park measures 180 feet, and along the other road, the park measures 215 feet.

The Bermuda triangle is a region of the Atlantic Ocean that connects Bermuda, Florida, and Puerto Rico. Find the area of the Bermuda triangle if the distance from Florida to Bermuda is 1030 miles, the distance from Puerto Rico to Bermuda is 980 miles, and the angle created by the two distances is 62°.

A yield sign measures 30 inches on all three sides. What is the area of the sign?

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

Find the area of a triangle with sides of length 18 in, 21 in, and 32 in. Round to the nearest tenth.

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

Find the area of a triangle with sides of length 20 cm, 26 cm, and 37 cm. Round to the nearest tenth.

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

$a=\frac{1}{2}\,\text{m},b=\frac{1}{3}\,\text{m},c=\frac{1}{4}\,\text{m}$

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

$a=12.4\text{ ft},\,b=13.7\text{ ft},\,c=20.2\text{ ft}$

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

$a=1.6\text{ yd},\,b=2.6\text{ yd},\,c=4.1\text{ yd}$

The sides of a parallelogram are 11 feet and 17 feet. The longer diagonal is 22 feet. Find the length of the shorter diagonal.

Two ships left a port at the same time. One ship traveled at a speed of 18 miles per hour at a heading of 320°. The other ship traveled at a speed of 22 miles per hour at a heading of 194°. Find the distance between the two ships after 10 hours of travel.

A triangular swimming pool measures 40 feet on one side and 65 feet on another side. These sides form an angle that measures 50°. How long is the third side (to the nearest tenth)?