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A right triangle has a hypotenuse of length 9 units and includes a 40° angle. What are the lengths of the other two sides?

5.79 units and 6.89 units
6.00 units and 6.71 units
11.75 units and 14.00 units
12.08 units and 13.49 units

Sagot :

Answer:

5.79 & 6.89 units

Step-by-step explanation:

Cos(40) =a/h

Cos(40) x 9=a

a=6.89

9^2 - 6.89^2 = a^2

33.5279 =a^2

Square root to get a to be 5.79

nuhulawal20

the lengths of the other two sides are 5.79 units and 6.89 unit.

Option A) is the correct answer.

What are the lengths of the other two sides?

Given the data in the question;

  • Hypotenuse side c = 9
  • Angle C = 90°
  • Angle A = 40°
  • Angle B = 180° - 90° - 40° = 50°
  • Length of side a = ?
  • Length of side b = ?

To get length of side a, we use the expression;

sinA = Opposite / Hypotenuse

sin40° = a / 9

a = sin40° × 9

a = 0.64278761 × 9

a = 5.79 units

sinB = b / hypotenuse

b = sin( 50° ) × 9

b = 0.766044443 × 9

b = 6.89 unit

Therefore, the lengths of the other two sides are 5.79 units and 6.89 unit.

Option A) is the correct answer.

Learn more about right angle triangles here: https://brainly.com/question/3772264

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