In ΔKLM, the measure of ∠M=90°, the measure of ∠L=76°, and LM = 99 feet. Find the length of KL to the nearest tenth of a foot.
1 answer:
Answer:
The length of KL is 409.2 foot
Step-by-step explanation:
Firstly, please check attachment for diagrammatic representation.
From the diagram, we can see that we are asked to calculate the value of the hypotenuse KL. Kindly note that the hypotenuse is the longest side of the right-angled triangle and it faces the angle 90 at all times.
Looking at what we have, we can see that we have adjacent and we are asked to calculate hypotenuse.
The trigonometric identity to use here is the Cosine
Cosine = length of adjacent/length of hypotenuse
cos 76 = 99/hypotenuse
hypotenuse = 99/cos76
hypotenuse = 99/0.24192
hypotenuse = 409.22 which is 409.2 to the nearest tenth of a foot
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Answer:
20 1/2 feet
Step-by-step explanation:
The total length is found by adding the lengths of the individual pieces. It can be easier if you use multiplication in place of repeated addition. You want ...
(2 × 5 feet) + (7 × 18 inches)
At some point in the process, you need to convert inches to feet. This is done by remembering that 12 inches = 1 foot. Dividing inches by 12 gives feet.
The above expression evaluates to
10 feet + 126 inches = 10 feet + (126/12) feet = 10 feet + 10.5 feet
= 20.5 feet
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A Google search box is a capable units converter and calculator.
The dimension that would give the maximum area is 20.8569
<h3>How to solve for the maximum area</h3>
Let the shorter side be = x
Perimeter of the semi-circle is πx
Twice the Length of the longer side
Length =
Total area =
area of rectangle + area of the semi-circle.
Total area =
When we square it we would have
This gives
From here we divide by 2
The maximum side would be at
This gives us 20.8569
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