The bell tower of the cathedral in Pisa, Italy, leans

$$5.6 ^ { \circ }$$

from the vertical. A tourist stands 105 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of the tower to be

$$29.2 ^ { \circ }$$

. Find the length of the tower to the nearest meter.

To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be

$$32 ^ { \circ }$$

. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is

$$35 ^ { \circ }$$

. Estimate the height of the mountain.

Find the radius r of the circle if an arc of length 15 m on the circle subtends a central angle of $5 \pi / 6.$

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that

$$\angle C A B = 48.6 ^ { \circ }$$

. He also measures CA as 312 ft and CB as 527 ft. Find the distance between A and B.

A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be

$$50 ^ { \circ }$$

. If the string is 450 ft long, how high is the kite above the ground?

Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 20$^{\circ}$, how far are you from the base of the plateau?

Graph $f(x)=3^{x-2}+1$ using transformations. What is the domain, range, and horizontal asymptote of f ?

The four cases in which we can solve a triangle are ASA SSA SAS SSS. In which of these cases can we use the Law of Sines to solve the triangle?

Contain rational equations with variables in denominators. For each equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.

$$\frac { 4 } { x } = \frac { 9 } { 5 } - \frac { 7 x - 4 } { 5 x }$$

From the top of a 200-ft lighthouse, the angle of depression to a ship in the ocean is $23 ^ { \circ }$.

How far is the ship from the base of the lighthouse?

Find the exact value of each expression. Do not use a calculator.

$$\cos \frac { 11 \pi } { 6 }$$

Let f and g represent differentiable functions such that f″ ≠ 0 and g″ ≠ 0. Prove that if f and g are positive, increasing, and concave upward on the interval (a, b) then fg is also concave upward on (a, b).

You divide a stack of fliers for a craft fair into 6 smaller stacks for volunteers to distribute. Each smaller stack contains 15 fliers. What is the total number of fliers distributed?

Write an equivalent first-order differential equation and initial condition for y.

$$y = - 1 + \int _ { 1 } ^ { x } ( t - y ( t ) ) d t$$