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Please help me with this

Please help me with this-example-1
User Yasin Yousif
by
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1 Answer

15 votes
15 votes

Answer:

(a) 7.6 cm

(b) 46.5 cm^2

Explanation:

(a)

The side you have marked as "Opp" is related to the given angle and side by ...

Sin = Opposite/Hypotenuse

Opp = Hyp·sin(43°) . . . . . . . . . . . multiply by hypotenuse

Opp ≈ (12 cm)·0.681998 ≈8.18398 cm

The value of x can be found using the Pythagorean theorem:

x^2 +3^2 = 8.18398^2

x = √(8.18398^2 -3^2) = √57.9775

x ≈ 7.614 cm

__

(b)

The bisector of the 38° angle will divide the triangle into two right triangles, each with a base of 4 and an opposite angle of 19°. The height of the triangle can be found from ...

Tan = Opposite/Adjacent

tan(19°) = (4 cm)/height

height = (4 cm)/tan(19°) ≈ 11.6168 cm

The area of a triangle is ...

A = 1/2bh . . . . . base b, height h

The area of the two right angled triangles will be ...

A = 2(1/2)(4 cm)(11.6168 cm) ≈ 46.5 cm^2

User Ursuleacv
by
3.1k points