Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

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Answer 1

1st picture: d. 45.7°

2nd picture: b. 6, 7, 8

3rd picture: c. 342 m.

Explanation:

1st picture:

Given:

In right angled triangle

Base=7.8

Opposite= 8

x=?

we have

`\boxed{\tt Tan\: x=(opposite)/(base)}`

`\tt Tan x= (8)/(7.8)`

`\tt x = Tan^(-1)(8)/(7.8)`

x=45.7°

Therefore, answer is d. 45.7°

`\hrulefill`

2nd Picture:

Note:

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

longest side is hypotenuse.

let's check a. 3,4,5

`5^2=3^2+4^2`

25=25

It is a right angled triangle.

let's check b. 6,7,8

8^2=6^2+7^2

64≠85

Since the left-hand side of the equation is not equal to the right-hand side, we can conclude that the triangle is not a right angled triangle.

Therefore, the only option that does not make a right angle triangle

is b. 6, 7, 8

`\hrulefill`

3rd Picture:

Given:

m∡Q=20°

m∡S= 90°

hypotenuse= 1000 meter

RS=?

We have:

`\tt Sin\: angle = (opposite)/(hypotenuse)`

`sin 20 =(RS)/(1000)`

doing criss cross multiplication:

RS = sin20*1000

RS=342 m

so, the answer is c. 342 m.