Answer:
(a) 7.6 cm
(b) 46.5 cm^2
Step-by-step 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
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(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
