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Answer: the length of the angle bisector of angle ∠A is 6 ft
Step-by-step explanation:
The diagram of the right angle triangle ABC is shown in the attached photo
Looking at triangle ABC,
cos θ = adjacent side/hypotenuse side
cos θ = 5/13 = 0.3846
θ = 67.38 degrees
The bisector of an angle divides it into two equal halves. The bisector is represented by line AD.
θ/2 = 67.38/2 = 33.69 degrees
Therefore,
Cos 33.69 = 5/AD
AD × Cos 33.69 = 5
AD = 5/Cos 33.69 = 5/0.832
AD = 6 ft
The longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.
<h3>How to measure diagonal of the cuboid?</h3>The length of the diagonal of the cuboid is found out using the following formula.
Here, (l) is the length of the cuboid, (w) is the width, and (h) is the height of the cuboid.
The wood has to buy to build a gate for backyard. The car trunk has the following dimensions (47 inches by 33 inches by 19.5 inches). Here, we have,
- Length (l)=47 in
- Width (w)=33 in
- Height (h)=19.5 in
The longest piece of wood which fits is equal to the length of diagonal of cuboid. Put the values in the formula,
Thus, the longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.
Learn more about the cuboid here;
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