Trigonometry
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree to the nearest foot.
33 ft
You have a triangle, and you know two of the angles measure 50 and 60. What is the measure of the third angle
70
The circumference of a circle is 24π. Find the area of this circle.
144π
Sarah is driving to her grandmother’s house. After 2 hours of driving, she has traveled 120 miles. After 4 hours of driving, she has traveled 240 miles. What is the slope (speed) of Sarah’s car in miles per hour?
A park ranger is designing a new trail on a grid map. The entrance of the trail is located at (3, 2). To avoid a protected marsh, the ranger needs to shift the entire trail layout 5 units to the right and 4 units up. What are the coordinates of the new trail entrance?
(8,6)
An 8 foot metal guy wire is attached to a broken stop sign to secure its position until repairs can be made. Attached to a stake in the ground, the guy wire makes an angle of 51º with the ground. How far from the foot of the stop sign is the stake, to the nearest tenth of a foot?
5 ft
In a right triangle, one of the acute angles measures 35. Since you know a right triangle has exactly one 90 angle, what is the measure of the other acute angle?
55
If the circumference and area of a circle are the same number, what is the diameter of the circle?
4
Liam starts a savings account. In Month 3, he has $150. In Month 5, he has $250. What is the rate of change (slope) of Liam’s savings per month?
50 a month
Sarah is standing on the left side of a completely still lake holding a bouquet of flowers. When she looks down into the water, she sees the flowers perfectly mirrored. If Sarah's hand holding the flowers is at the coordinate (2, 8), where does the reflection of the flowers appear in the water?
(2,-8)
On a windy day, a 90 foot rope tightly secures a hot air balloon to a stake in the ground. From the balloon, the angle of depression of the stake is 62º. Find, to the nearest foot, the height of the balloon, assuming the wind to be constant.
79
You walk 400 meters west, and your friend walks 300 meters south from the exact same starting point. What is the direct straight-line distance between you and your friend?
500
An advertising sign has dimensions as shown at the right. Consider the top of the sign to be a semicircle.
a) A neon strip of lighting is to be placed around the outer edge of the sign. How long a strip of neon will be needed?
(to nearest tenth of foot)
19.7
A bucket is catching water from a leaky faucet. After 10 minutes, there are 5 inches of water in the bucket. After 20 minutes, there are 10 inches of water. What is the slope of the water level over time?
0.5
A baker takes a square cake out of the oven and places it on a rotating decorating table. The cake's top-left corner is initially pointing at 12 o'clock. The baker spins the table exactly 1/4 of a turn clockwise. Which direction is the original top-left corner of the cake now pointing?
east or 3:00
From point P on the ground, the angle of elevation of an airplane is 23º. The altitude of the plane is 1200 meters. What is the distance from point P to the airplane, to the nearest tenth of a meter?
3071.2
15
How far does a wheel with a radius of 15 inches travel in 20 revolutions? Express answer to the nearest foot.
157
A pizza shop charges $10 for a basic cheese pizza, plus $2 for every extra topping you add. If x is the number of toppings and y is the total cost, what is the slope of this equation?
2
A graphic designer is shrinking a digital logo for a business card. The original rectangular logo has a width of 12 inches and a height of 8 inches. She resizes the logo using a scale factor of 1/2. What are the new dimensions of the logo?
Width is 6 inches, Height is 4 inches
From the hay loft door, Ted sees his dog on the ground. The angle of depression of the dog is 40º. Ted's eye level is 16 feet above the ground. How many feet must the dog walk to reach the open barn door directly below Ted (to the nearest foot)?
19
Find the angle measures of a triangle if the second angle measures 10 degrees less than twice the first, and the third angle measures 25 degrees more than the second.
35,60,85
Given the equation of a circle to be
x2 + y2 -10x +14y + 10 = 0,
a) find the center and radius of the circle.
center (5,-7), radius 8
100
A point on a game board is located at (-3, 4). To capture a game piece, the point must first be reflected across the y-axis, and then translated 2 units down. What are the final coordinates of the point?
(3,2)