Answer:
a = 20; b = 2√101
Step-by-step explanation:
The triangle at upper left and the one at lower right are similar. Ratios of corresponding sides are equal, so ...
200/a = a/2
400 = a^2
√400 = 20 = a
Then, by the Pythagorean theorem, the value of b can be found:
b = √(a^2 + 2^2) = √(400 +4) = √4·√101
b = 2√101
Rounded to 1 decimal place
Answer:
5.0 ft - 5.6 ft
Step-by-step explanation:
Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.
Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;
Tan α = opposite side length/adjacent length
Tan 40°= h/8
h= 8 tan 40° = 6.71 ft
Applying the cosine of an angle formula to find the length of the sliding side
Cosine β = adjacent length /hypotenuse
Cosine 40°= 8/ sliding side length
sliding side length = 8/cosine 40° =10.44 ft
Checking the perimeter = 10.44 +8+6.71= 25.15 ft
This is more than the total lengths of the boards, so you need to adjust the height as;
24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft
h≤ 5.6 ft
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