Exam 7: Applications of Trigonometric Functions

Choose the one alternative that best completes the statement or answers the question. Solve the triangle. - $\mathrm { b } = 4 , \mathrm { c } = 6 , \alpha = 80 ^ { \circ }$

Solve the problem. -The distance from home plate to dead center field in a certain baseball stadium is 402 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center Field?

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\sin \mathrm { A }$ when $a = 8$ and $b = 7$ .

Solve the problem. -A ladder leans against a building that has a wall slanting away from the ladder at an angle of 96° with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall, How tall is the ladder to the nearest foot?

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\tan \mathrm { B }$ when $\mathrm { a } = 4$ and $\mathrm { b } = 5$ .

Solve the triangle. Find the angles  and  first. -

Solve the triangle. Find the angles  and  first. - $\mathrm { a } = 19 , \mathrm {~b} = 16 , \mathrm { c } = 11$

Solve the triangle. - $\beta = 40 ^ { \circ } , \quad \gamma = 10 ^ { \circ } , \quad \mathrm { b } = 5$

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 13 }$ and $\mathrm { c } = 10$ .

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. Do not use a calculator. - $\csc ^ { 2 } 65 ^ { \circ } - \tan ^ { 2 } 25 ^ { \circ }$

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. - $\mathrm { a } = 4 , \quad \mathrm {~b} = 5 , \quad \alpha = 70 ^ { \circ }$

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\cot \mathrm { A }$ when $\mathrm { b } = 5$ and $c = 6$ .

Solve the problem. -An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as $14 ^ { \circ }$ and $24 ^ { \circ }$ . How high is the airplane?

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. Do not use a calculator. - $\tan 15 ^ { \circ } - \frac { \cos 75 ^ { \circ } } { \cos 15 ^ { \circ } }$

Solve the triangle. -

Choose the one alternative that best completes the statement or answers the question. Find the area of the triangle. If necessary, round the answer to two decimal places. - $a = 13 , b = 15 , c = 13$

Choose the one alternative that best completes the statement or answers the question. Solve the triangle. - $\mathrm { a } = 4 , \mathrm { c } = 3 , \beta = 90 ^ { \circ }$

Find the area of the triangle. If necessary, round the answer to two decimal places. -

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Find the area of the shaded portion ( see illustration) of a circle of radius $25 \mathrm {~cm}$ , formed by a central angle of $115 ^ { \circ }$ . Round your answer to the nearest square $\mathrm { cm }$ . [Hint: Subtract the area of the triangle from the area of the sector of the circle to obtain the area of the shaded portion.]

Solve the problem. -A box has dimensions $2 ^ { \prime \prime } \times 3 ^ { \prime \prime } \times 4 ^ { \prime \prime }$ . (See illustration.) Determine the angle $\theta$ formed by the diagonal of the $2 ^ { \prime \prime } \times 3 ^ { \prime \prime }$ side and the diagonal of the $3 ^ { \prime \prime } \times 4 ^ { \prime \prime }$ side. Round your answer to the nearest degree.