7.01 Apply the Pythagorean theorem
Calculate the value of c for the following triangles:
Calculate the value of the variable for the following triangles:
Consider the given triangle:
Find the length of the hypotenuse.
Find the perimeter of the triangle.
Consider the given triangle:
Find the following, rounding your answer to two decimal places:
The value of x.
The value of y.
The length of the base of the triangle.
For each of the following figures, find the length of the unknown side x, correct to two decimal places:
Given the following diagram, find the following correct to two decimal places:
The value of x.
The value of y.
Consider the following trapezoid:
Find the value of a.
Find the value of b.
Find x, correct to two decimal places.
Find the perimeter of the trapezoid, correct to two decimal places.
VUTR is a rhombus with perimeter 112\text{ in}. The length of diagonal \overline{RU} is 46\text{ in}.
Find the length of \overline{VR}.
Find the length of \overline{RW}.
Find the length of \overline{VW}, correct to two decimal places.
Now, find the length of the other diagonal \overline{VT}. Round your answer to two decimal places.
Find the value of k in the following figure. Round your answer to two decimal places.
Determine whether each of the following sets of three lengths could represent the sides of a right triangle:
4, \, 3, \, 2
4, \, 3, \, 5
6, \, 8, \, 10
5, \, 12, \, 13
If x, y, and z are three sides of a right triangle, will side lengths of 6 x, 6 y and 6 z make a right triangle as well?
The following pair of numbers are lengths of the shorter sides of a right triangle. For each pair:
Find the corresponding primitive triple.
Now, find the length of the hypotenuse in the triangle.
6 and 8
15 and 36
24 and 45
32 and 126
Consider a right triangle with side length 40 \text{ cm} and hypotenuse 85 \text{ cm}.
Find the corresponding primitive triple.
Now, find the length of the unknown side in the triangle.
Consider the following triangle:
Show that the triangle is a right triangle.
State the size of the two acute angles.
Show that any triangle whose side lengths are k, k and k \sqrt{2} are the sides of a right triangle.
Peter knows the two smallest numbers in a Pythagorean triple are 3 and 4. What number does Peter need to complete the triple?
Sean knows the two largest numbers in a Pythagorean triple are 41 and 40. What number does Sean need to complete the triple?
The following pairs of numbers are the smallest values in a Pythagorean triple. Find the largest value, c.
22 and 120
16 and 30
15 and 112
20 and 99
If 100 and 96 are the two largest values in a Pythagorean triple, what is the smallest value of the triple?
Complete the following Pythagorean triples:
28, \, ⬚, \, 53
14, \, 48, \, ⬚
⬚, \, 24, \, 26
24, \, ⬚, \, 145
Consider the triple \left(9, 12, 15\right).
Evaluate 9^{2} + 12^{2}.
Evaluate 15^{2}.
Is \left(9, 12, 15\right) a Pythagorean triple?
Find the corresponding primitive triple.
Consider the triples \left(8, 15, 17\right) and \left(16, 30, 34\right).
Is \left(8, 15, 17\right) a Pythagorean triple? Justify your answer.
Is \left(16, 30, 34\right) a Pythagorean triple? Justify your answer.
Multiply each of the values in \left(8, 15, 17\right) to get a new triple.
Plot the triangles for each of the three triples on a coordinate plane. For each triangle, plot one of the vertices on the origin, the shortest side on the x-axis and another side on the y-axis.
Determine whether or not the three triangles are similar.
Iain’s car has run out of gas. He walks 12 \text{ mi} west and then 9 \text{ mi} south looking for a gas station.
If he is now h \text{ mi} directly from his starting point, find the value of h.
Consider a cone with slant height 13 \text{ m} and perpendicular height 12 \text{ m}:
Find the length of the radius, r, of the base of this cone.
Now, find the diameter of the base of the cone.
A soda can has a height of 11 \text{ cm} and a radius of 4 \text{ cm}.
Find L, the length of the longest straw that can fit into the can. Round your answer down to the nearest centimeter, to ensure it fits inside the can.
Two flag posts of height 12 \text{ m} and 17 \text{ m} are erected 20 \text{ m} apart.
Find the length, l, of the string needed to join the tops of the two posts. Round your answer to one decimal place.
A farmer wants to build a fence around the entire perimeter of his land as shown in the following diagram. The fencing costs \$37 per meter.
Find the value of x. Round your answer to two decimal places.
Find the value of y. Round your answer to two decimal places.
How many meters of fencing does the farmer require, if fencing is sold by the meter?
At \$37 per meter of fencing, how much will it cost him to build the fence along the entire perimeter of the land?
