Answer:
24.43 units to the nearest hundredth.
Step-by-step explanation:
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We first need to find the lengths of sides PN and MN. tan 58 = 8/PN PN = 8 / tan58 = 5 . sin 58 = 8 / MN MN = 8 / sin 58 = 9.43. So the perimeter = 8 + 5 + 9.43 = 22.43.
The perimeter of ∆MNP is 22.4 units.
The triangle formed is a right angle triangle because one of the angle of the triangle is 90°.
The perimeter of the triangle ΔMNP is the sum of the whole side of the triangle.
let's use trigonometric ratio to find the side PN and use Pythagoras's theorem to find the side MN(hypotenuse).
Therefore,
tan 58°= opposite / adjacent
tan 58° = 8 / PN
PN = 8 / 1.60033452904
PN = 4.99895481527
PN ≈ 5.0 units
Therefore, using pythagora's to find MN
MN² = PM² + PN²
MN² = 8² + 5²
MN = √89
MN = 9.43398113206
MN ≈ 9.4
Perimeter = 8 .0 + 5.0 + 9.4 = 22.4
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