Question

a ladder 15 m long just reaches the top of a vertical wall if the ladder makes an angle of 60 with the wall, find the height of the wall​

Answer 1

Answer:

7.5m

Step-by-step explanation:

Draw the rough diagram which shows the details of the problem

Diagram shows a right angled triangle ABC. Right angle at

Let the length of ladder AC=15m

(hypotenuse)

Angle between ladder and wall < BCA=60°

Height of the wall=BC

From triangle ABC

Sin

Sin 30=BC/15

1/2=BC/15

15/2=BC

7.5=BC

Therefore,

Height of the wall=BC=7.5m

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Answer 2

Given data:-

• A ladder 15m long, just reaches the top of a vertical wall.
• The ladder makes an angle of 60° with the wall.

Assumption:-

• Let, AB be the wall which is perpendicular to the ground. and CA be the ladder of length 15m.{Hence angle ABC = 90°}
• Let, angle CAB is of 60° {according to figure and given}.

Solution:-

According to assumption & figure

—› CA = hypotenuse

To find the height of the wall.

{We need to take, sin ratio with opposite angle of wall}

Hence, we need to find opposite angle of wall. and opposite angle of wall is angle BCA.

To find angle ABC :-

We know, "Sum of all angles of triangle is equal to 180°. hence,

—› angle ABC + angle BCA + angle CAB

= 180

—› 90 + angle BCA + 60 = 180

—› angle BCA + 150 = 180

—› angle BCA = 180 - 150

—› angle BCA = 30°

According to assumption & figure

—› AB = opposite side to angle angle BCA

Now, we use sin ratio with angle BCA, where, θ = 30°

—› Sin( θ ) = {opposite side}/{hypotenuse}

—› Sin( 30 ) = AB/CA

—› 1/2 = AB/15 i.e.

—› AB = 15/2

—› AB = 7.5 m

Hence, the height of wall is 7.5m.