Exam 7: Applications of Trigonometric Functions

Graph the damped vibration curve for 0 $0 \leq t \leq 2 \pi$ . -An object is suspended from a coiled spring. It is pulled downward and released. The position P above or below its rest position after t seconds is given by $\mathrm { P } = - \mathrm { e } ^ { - \mathrm { x } / 2 \pi } \cos \mathrm { x }$ Find all values of $( 0 \leq \mathrm { t } < 4 \pi )$ ) for which the object is at the rest position and graph the equation for $0 \leq t < 4 \pi$

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $a = 5 , \beta = 35 ^ { \circ }$ ; Find $b , c$ , and $\alpha$ .

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 $\tan B$ when $a = 4$ and $b = 5$ .

Solve the problem. -A famous golfer tees off on a long, straight 471 yard par 4 and slices his drive 18° to the right of the line from tee to the hole. If the drive went 290 yards, how many yards will the golfer's second shot have to be to reach the Hole?

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 $\cot A$ when $a = 3$ and $c = 4$ .

Solve the triangle. Find the angles α and β first. - $a = 8 , b = 13 , c = 17$

Solve the problem. -A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot.

Find the area of the triangle. If necessary, round the answer to two decimal places. -Penrose tiles are formed from a rhombus WXYZ with sides of length 1 and interior angles 72° and 108°. (Refer to the illustration.) A point O is chosen on the diagonal 1 unit from Y. Line segments OX and OZ are drawn to the other vertices. The two resulting tiles are called a kite (figure OXYZ) and a dart (figure OXWZ). Find the area of the kite tile and the dart tile, correct to the nearest 0.01.

Solve the problem. -

Solve the problem. -Yosemite Falls in California consists of three sections: Upper Yosemite Fall (by itself one of the ten highest waterfalls in the world), the Middle Cascade, and Lower Yosemite Fall. From a footbridge across the creek 2500 feet from the falls, the angles of elevation to the top and bottom of Upper Yosemite Fall are 45.74° and 24.42°, respectively. How high is the total series of three falls? How high is Upper Yosemite Fall? Round your answers 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 $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 13 }$ and $\mathrm { c } = 10$ .

Solve the triangle. Find the angles α and β first. - $\mathrm { a } = 8 , \mathrm {~b} = 8 , \mathrm { c } = 7$

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

Solve the problem. -A flagpole is perpendicular to the horizontal but is on a slope that rises 10° from the horizontal. The pole casts a 43-foot shadow down the slope and angle of elevation of the sun measured from the slope is 36°. How tall is the Pole? Round your answer to the nearest 0.1 foot.

Solve the problem. -A straight trail with a uniform inclination of 18° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 7,100 feet. What is the length of the trail (to the nearest foot)?

Solve the triangle. Find the angles α and β first. -

Solve the problem. - $\mathrm { a } = 4 , \mathrm { c } = 3 , \beta = 90 ^ { \circ }$

Solve the problem. -A forest ranger at Lookout A sights a fire directly north of her position. Another ranger at Lookout B, exactly 2 kilometers directly west of A, sights the same fire at a bearing of N41.2°E. How far is the fire from Lookout A? Round your answer to the nearest 0.01 km.

Solve the problem. -A sailboat leaves port on a bearing of S72°W. After sailing for two hours at 12 knots, the boat turns 90° toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from port? Round your answer to the nearest 0.1°.

Solve the problem. -A famous golfer tees off on a straight 390 yard par 4 and slices his drive to the right. The drive goes 280 yards from the tee. Using a 7-iron on his second shot, he hits the ball 180 yards and it lands inches from the hole. How Many degrees (to the nearest degree) to the right of the line from the tee to the hole did he slice his drive?