Question

An 18-foot ladder leaning against a wall makes an angle of elevation of 70° with the ground. How far up the wall is the ladder, to the nearest foot?

A.7 ft.
B.6 ft.
C.19 ft.
D.17 ft.

Answer 1

Answer:

The ladder is the hypotenuse of a right-angle triangle.

Use the Pythagorean Theorem.

Step-by-step explanation:

Let AC denote the ladder and B be foot of the wall.

Let the length of the ladder AC be x metres.

Given: (1)∠CAB = 70°

           (2)AB = 5.4m

In the right ∠CAB, cos 70° = $AB/AC$

AC = $AB/cos 70$°

x = $5.4/cos 70$

x = 15.788543761

x = 17 ft.

Its D I think

Sorry If I am wrong but I think this will be correc

Answer 2

Answer:

The correct answer is option (B), 6 ft. The ladder is placed 6 foot away from the foot of the wall on the ground.

Explanation:

• Given that the length of the ladder is 18 foot. It is leaning against a wall makes an angle of elevation of 70° with the ground.

• We have to find how far the ladder is placed away from the foot of the wall on the ground. That is to the nearest foot.

• By using the given data, we can consider a right angled triangle.
• In the right angled triangle ABC, where the ladder is the hypotenuse of right angled triangle, the height of wall from the ground to the top end of ladder is the perpendicular of right angled triangle and the ground length from foot of the wall to bottom end of the ladder is the base of right angled triangle.
• We need how far the ladder is placed away from the foot of the wall on the ground, which means the base of right angled triangle.

• Let AC denote the ladder (hypotenuse) and B be foot of the wall. So that CB is the perpendicular and we want to find AB (base). From the given ladder length it is clear that hypotenuse of triangle = 18 foot.
• Also, the ladder leaning against a wall makes an angle of elevation of 70° with the ground, which means ∠CAB = 70°.

• Now we have two measurements.

i.e., Hypotenuse = 18 foot

      ∠CAB = 70°.

• We know that in a right angled triangle, cos Ф = $\frac{Adjacent Side}{Hypotenuse}$

• Consider the Δ ABC, cos  (∠CAB) = $\frac{Base}{Hypotenuse}$

cos 70° = $\frac{AB}{AC}$

⇒ cos 70° = $\frac{AB}{18}$

⇒ AB = 18 × cos 70°

⇒ AB ≅ 6 foot.

AB = Base = 6 foot.

• Therefore, the correct answer is option (B), 6 ft. The ladder is placed 6 foot away from the foot of the wall on the ground.

To know more, go through the links;

https://brainly.in/question/47692999

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