Exam 2: Acute Angles and Right Triangles

Solve the problem. -A 35-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place when necessary.

Solve the right triangle. -A = 19° 17´, c = 287 ft, C = 90° Round side lengths to two decimal places, if necessary.

Solve the problem. -Find h as indicated in the figure. Round to the nearest foot.

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\sin \theta = - \frac { \sqrt { 2 } } { 2 }$

The number represents an approximate measurement. State the range represented by the measurement. -24.35 k

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\tan \mathrm { B }$ when $\mathrm { a } = 48$ and $\mathrm { c } = 50$ .

Find the exact value of the expression. - $\sec 240 ^ { \circ }$

Find the exact value of the expression. - $\csc \left( - 2460 ^ { \circ } \right)$

Determine whether the statement is true or false. -cos 60° = cos 180° - cos 120°

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is 13°11'. If the base of the cliff is 1683 feet from the boat, how high is the cliff (to the nearest foot)?

Solve the problem. -The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ϴ where W is the weight of the car and ϴ is the angle of the hill's grade (ϴ > 0 for uphill travel, ϴ < 0 For downhill travel). A 2025-lb car has just rolled off a sheer vertical cliff (ϴ = -90°). What is the Car's grade resistance?

Find the exact value of the expression. -sec 150°

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\tan B$ when $b = 8$ and $c = 9$ .

Solve the problem. -The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$ , where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). Find the weight of the car (to the nearest pound) that is traveling on $\mathrm { a } - 2.2 ^ { \circ }$ downhill grade and which has a grade resistance of $- 153.55 \mathrm { lb }$ .

Find the reference angle for the given angle. -236.6°

Solve the right triangle. -a = 2.6 in., A = 49.8°, C = 90° Round values to one decimal place.

Solve the problem. -Find the exact value of x in the figure.

Decide whether the statement is true or false. -tan 23° < tan 4°

Decide whether the statement is true or false. -tan 28° > cot 28°

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\tan \left( \theta + 22 ^ { \circ } \right)$