삼각함수 전체 문제

Brian’s house is on a corner lot. Find the area of the front yard if the edges measure 40 and 56 feet, as shown in (the referenced figure).

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?

Naomi bought a dining table whose top is in the shape of a triangle. Find the area of the table top if two of the sides measure 4 feet and 4.5 feet, and the smaller angles measure 32° and 42°, as shown in (the referenced figure).

If you are looking for a missing side of a triangle, what do you need to know when using the Law of Cosines?

If you are looking for a missing angle of a triangle, what do you need to know when using the Law of Cosines?

Explain what $s$ represents in Heron’s formula.

Explain the relationship between the Pythagorean Theorem and the Law of Cosines.

When must you use the Law of Cosines instead of the Pythagorean Theorem?

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\gamma =41.2^\circ ,a=2.49,b=3.13$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\alpha =120^\circ ,b=6,c=7$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\beta =58.7^\circ ,a=10.6,c=15.7$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\gamma =115^\circ ,a=18,b=23$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\alpha =119^\circ ,a=26,b=14$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\beta =67^\circ ,a=49,b=38$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\alpha =43.1^\circ ,a=184.2,b=242.8$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\alpha =36.6^\circ ,a=186.2,b=242.2$

For the following exercises, assume $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ is opposite side $c.$ If possible, solve each triangle for the unknown side. Round to the nearest tenth.

$\beta =50^\circ ,a=105,b=45$

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=42,b=19,c=30;$ find angle $A.$

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=14,\,b=13,\,c=20;$ find angle $C.$