Solve each system of equations using substitution. a=5b+8 a=-10b-7
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From the setup of the problem, the "length of the top of the bookcase, measured along the attic ceiling" will be the hypotenuse of a right triangle, the length "AB". We have both the angle between AB and AC and the length of AC (3.24 meters), so we can use trigonometric identities.
The cosine of the 40 degree angle between AB and AC is equivalent to the length of AC divided by the length of AB. Equivalently, we have:
where "h", the hypotenuse, is the length we want. Rearranging the formula to solve for h we have that
which is 4.2295... meters. Converting to centimeters (multiplying by 100) we have that h = 422.95... centimeters, or if we round the value, h = 423 centimeters.
<span>The complete question is shown in the attached image
<u><em>Answer:</em></u>
measure angle H = 42</span>°<span>
<u><em>Explanation:</em></u>
<u>There is a theorem that states that:</u>
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"
<u>In the given, we have:</u>
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H
<u>Based on the above rule:</u>
measure angle E = measure angle D + measure angle H
<u>We are given that:</u>
angle E = 87</span>°<span>
angle D = 45</span>°<span>
<u>Substitute with the givens in the above rule and solve for the measure of angle H as follows:</u>
angle E = angle D + angle H
87</span>°<span> = 45</span>°<span> + measure angle H
measure angle H = 87</span>°<span> - 45</span>°<span>
measure angle H = 42</span>°<span>
Hope this helps :)</span>
<u><em>Answer:</em></u>
measure angle H = 42</span>°<span>
<u><em>Explanation:</em></u>
<u>There is a theorem that states that:</u>
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"
<u>In the given, we have:</u>
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H
<u>Based on the above rule:</u>
measure angle E = measure angle D + measure angle H
<u>We are given that:</u>
angle E = 87</span>°<span>
angle D = 45</span>°<span>
<u>Substitute with the givens in the above rule and solve for the measure of angle H as follows:</u>
angle E = angle D + angle H
87</span>°<span> = 45</span>°<span> + measure angle H
measure angle H = 87</span>°<span> - 45</span>°<span>
measure angle H = 42</span>°<span>
Hope this helps :)</span>