Answer:
18. h = 14.4
19. h = 4.23
20. h = 15.28
21. h = 11.46
All answers are rounded to two decimal places.
Step-by-step explanation:
18. To find the height if you know all 3 sides. Multiply sides a & b, and divide the product by c.
x = (a * b)/c
x = (18 * 24)/30
x = 432/30
x = 72/5
x = 14.4
19. We know that the entire length of the hypotenuse is 27. However, 24 is needed here. That's 8/9 of 27, so 80 degrees is one of the angles. So we need to find the hypotenuse first. That can be done like this: b/sin(β)
24/sin(80)
24/0.98480775
24/1 * 4000000/3939231
8/1 * 4000000/1313077
32000000/1313077
24.3702388
Now to find the first leg, which will be the height of the entire triangle.
x = √c² - b²
x = √24.3702388² - 24²
x = √593.908539 - 576
x = √17.908539
x = 4.23184818
x = 4.23
20. This one requires similar work to #19, but the hypotenuse of the smaller triangle is x.
20/sin(60)
20/0.8660254
20/1 * 5000000/4330127
100000000/4330127
23.0940109
√23.0940109² - 20²
√533.333339 - 400
√133.333339
11.5470056
î The answer above is leg 2 of the smaller triangle.
x = √10² + 133.333339
x = √100 + 133.333339
x = √233.33339
x = 15.2752525
x = 15.28
21. There is no need to figure out what the height is. The entire triangle is 45-45-90.
x = (√18² + 18²) - 15
x = (√324 + 324) - 15
x = (√648) - 15
x = 25.46 - 15
x = 11.46
Answer:
2, 16
Step-by-step explanation:
1) given that those two lines are parallel, we can deduce that 9/45=x/75.
9/45 simplifies to 1/5 so 1/5 = x/75. Cross multiply to get this: 5x = 75.
Divide both sides by 5 to get x.
Final answer: x = 15
2) Again, we can set up a proportion to solve for x because we know the lines are parallel. 24/36=x/12. 24/36 simplifies to 2/3 so 2/3=x/12. Cross multiply to get this: 3x = 24. Divide both sides by 3 to get x.
Final answer: x = 8
Answer: D’Andrea
Explanation: 93/3 = 31
176/4=44
215/5= 43
111/3= 37
44 is greater than 31, 43, and 37 therefore D’Andrea does the most sit-ups per minute.
