A rectangle has a perimeter of 66 meters and a height of 14.2 meters. What is the length of the base?
1 answer:
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Answer:
Step-by-step explanation:
a.
The angles given are 62° and 90°.
We know sum of angles in any triangle is 180° so the third angle must be 180-90-62 = 28°
We can find the sides if we know trigonometric functions
sin28° = opp. side/ hypothenuse = CA/BA = 8/BA
BA = 8/sin 28° ≈ 17
tan62°= opp.side/adj.side= BC/AC = BC/8
BC = 8 · tan62° ≈ 15
b.
We are given 2 sides 8.5 and 6.5 and that one angle is right, so the triangle is a right triangle, therefore we can apply Pythagorean Theorem to find the third side.
6.5² +FD² = 8.5², subtract 6.5² from both sides
FD² = 8.5²- 6.5², square and combine like terms
FD² = 30, square-root both sides
FD = √30
FD ≈ 5.47722, round to the nearest tenth
FD ≈ 5.5
We can find the angles if we know trigonometric functions.
sin ∡D = FE/DE = 6.5/8.5
∡D = sin^-1 (6.5/8.5)
∡D ≈ 49.9°
cos ∡E = FE/DE = 6.5/8.5
∡E = cos^-1 (6.5/8.5)
∡E ≈ 40.1°
