Answer:
acute: 7, 9
right: 8, 10
obtuse: 5, 6
Step-by-step explanation:
When you have a number of identical calculations to do, it is convenient to do them in a spreadsheet. You only need to enter the formula once and copy it as many times as needed.
The attachment shows the "sum of squares" calculation and comparison to the square of the longest side. When the sum is too small, the longest side is longer than needed for a right angle, so the triangle is obtuse. When the sum is too great, the longest side is too short for a right angle, so the triangle is acute.
We have skipped the tedious arithmetic and shown the results in the attached table.
Okay, so Sang is standing 20 yards away from one corner, and Jazmin is standing 99 yards away from the same corner. If this is a rectangle (I like visuals, so I'll use them to explain), then:
99ft
A ------------------------- B
| |
20 ft | |
| |
C -------------------------- D
The question is asking you to solve for the diagonal line between points C and B. If you imagine a line there, you actually have the rectangle split into two triangles. So if you have triangle ABC, side CB would be the longest line, or the hypotenuse. That means you can use the Pythagorean Theorem to solve the problem.
A^2 + B^2 = C^2
99^2 + 20^2 = C^2
9,801 + 400 = C^2
10,201 = C^2
Now you solve for the square root of 10,201 to get C.
sqr (10,201) = C
C = 101 yards