Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

c. 75 ft

taking 20 as reference angle

cos 20 = b/h = x/80

so, x = cos 20 * 80 = 75.17

so, closest is 75

The ranges of length should be (43-24) = 19 in. to

43+24 = 67 in. so ans. is 20,21,29.

b = 14/2 = 7 cm as its folded in half. h = 14 cm

now,

p² =h² + b²

or, p² = 14² + 7²

so, p =

`7 √(3)`

answer is a.

`7 √(3)`

Answer 2

• 1st question: c. 75 ft
• 2nd question:b. 20, 21, 29
• 3rd question:
  `\sf a.\:  7√(3) \:cm`

Explanation:

For 1st Question:

Given:

angle =20°

In right angle with respect to angle

Hypotenuse (h) = 80 ft

Adjacent or base(b) = x

Since Relation between Adjacent or base(b) and hypotenuse by cosine angle rule.

We have,

`\sf Cos\: angle = (Base)/(Hypotenuse)`

Substituting value

`\sf Cos 20^\circ = (x)/(80)`

Doing Criss cross multiplications

`\sf x= Cos 20^\circ * 80`

`\sf x \approx 75 ft`

Therefore, answer is c. 75 ft

`\hrulefill`

For 2nd question:

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

So, the range of possible lengths for the third side is:

`\sf x > 43 - 24 = 19\\\sf x < 43 + 24 = 67`

Therefore, the answer is b. , 20,21, 29

`\hrulefill`

For 3rd question:

Given:

angle = 60°

In right angle with respect to angle

Hypotenuse (h) = 14 cm

since all sides of equilateral triangle are equal.

Opposite or perpendicular = x

Since Relation between Opposite or perpendicular and hypotenuse by cosine angle rule.

Since Relation between opposite or perpendicular and hypotenuse by sine angle rule.

We have,

`\sf Sin \:\:angle = (Perpendicular)/(Hypotenuse)`

Substituting value

`\sf Sin 20^\circ = (x)/(14)`

Doing Criss cross multiplications

`\sf x= Sin 60^\circ * 14`

`\sf x \approx 7√(3) cm`

Therefore, answer is
`\sf a.\: 7√(3) \:cm`