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Dominik [7]
3 years ago
12

The height to the base of an isosceles triangle is 12.4m, and its base is 40.6m. What are the measurement of the angles of the t

riangle and the length of its legs?
*m is meters

Mathematics
2 answers:
Vsevolod [243]3 years ago
5 0

Answer:

  • angles: 31.42°, 31.42°, 117.16°
  • legs: 23.79 m

Step-by-step explanation:

The base angles can be found from the definition of the tangent function:

  tan(base angle) = height/(half-base length)

  base angle = arctan(12.4/20.3) ≈ 31.418°

Then the apex angle is double the complement of this:

  apex angle = 2(90° -31.418°) ≈ 117.164°

The base angles are 31.42°, and the apex angle is 117.16°.

__

The leg lengths can be computed from the Pythagorean theorem applied to the altitude and the half-base length.

  leg length = √(12.4² +20.3²) = √565.85 ≈ 23.789 . . . . meters

The length of the legs is about 23.79 m.

Mariana [72]3 years ago
3 0

angles: 31.42°, 31.42°, 117.16°

legs: 23.79 m

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