Question

Solve the question below

Answer 1

The answer is below

Explanation:

1) A triangle is a polygon with three sides and three angles. There are different types of triangles such as obtuse, scalene, right angle, equilateral and isosceles triangle.

Given that triangle ABC is right angled and AC = 25 cm = hypotenuse and BC = 15 cm. Using Pythagoras:

AC² = BC² + AB²

25² = AB² + 15²

AB² = 25² - 15²

AB² = 400

AB = √400

AB = 20 cm

Using sine rule:

`(sin(B))/(AC)=(sin(A))/(BC)=(sin(C))/(AB)\\\\But\ \angle B= 90^o(right\ angle)\ hence:\\\\ (sin(B))/(AC)=(sin(A))/(BC)\\\\(sin(90))/(25)=(sin(A))/(15)\\\\sin(A)=(sin(90))/(25)*15\\\\sin(A)=0.6\\\\A=sin^(-1)(0.6)\\\\A=36.87^o`

2)

Using Pythagoras:

hypotenuse² = 8² + 6²

hypotenuse² = 100

hypotenuse = √100

hypotenuse = 10

Using sine rule:

`(sin(x))/(8)=(sin(90))/(10)\\\\sin(x)=(sin(90))/(10)*8\\\\sin(x)=0.8\\\\x=sin^(-1)(0.8)\\\\x=53.13 ^o`