Exam 2: Acute Angles and Right Triangles

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 14°57'. If the dam is 1286 feet above the level of the river, how far is the boat from the base of the dam (to the Nearest foot)?

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { a } = 10.9 \mathrm {~cm} , \mathrm {~b} = 21.7 \mathrm {~cm}$ Round the missing side length to one decimal place.

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 $\cos A$ when $a = 5$ and $b = 3$ .

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -tan ϴ = 0.83799703

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -tan 55°50´

Find the reference angle for the given angle. -39°

The number represents an approximate measurement. State the range represented by the measurement. -17.3 m

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

Solve the problem. -An airplane travels at 195 km/h for 1 hr in a direction of 287° from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

Determine whether the statement is true or false. -cos 135° = cos 225° cos 90° + sin 225° sin 90°

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cot 40°44´

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -csc ϴ = 1.7437345

Solve the problem. -A ship travels 82 km on a bearing of 24°, and then travels on a bearing of 114° for 162 km. Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Evaluate. - $\cos ^ { 2 } 315 ^ { \circ } - \sin ^ { 2 } 270 ^ { \circ } + 4 \tan ^ { 2 } 30 ^ { \circ }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -cot 31.1°

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\cos \theta = \frac { 1 } { 2 }$

Solve the problem for the given information. -Find the equation of a line passing through the origin and making a 45° angle with the positive x-axis.

Find the exact value of the expression. - $\tan 2130 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. -cot 45°

Solve the problem. -Snell's Law states that $\frac { \mathrm { c } _ { 1 } } { \mathrm { c } _ { 2 } } = \frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } }$ . Use this law to find the requested value. If $\mathrm { c } _ { 1 } = 8 \times 10 ^ { 8 }$ , $c _ { 2 } = 6.14 \times 10 ^ { 8 } , \theta _ { 2 } = 36 ^ { \circ }$ , find $\theta _ { 1 }$ . Round your answer to the nearest degree.