Question

In the given figure, ΔABC is right angled at B and ΔBRS is right angled at R. If AB=18cm, BC= 7.5cm and RS = 5cm, find the value of
(a) tanX°
(b) sinY°

Answer 1

Answer:

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Answer 2

the value of Sin y = 5 / 13

the value of Sin y = 5 / 13 And value of Tan x = 6 / 5

Given: BC = 7.5 cm

AB = 18 cm

RS = 5cm

To find: Tan x

Sin y

Solution:

We know Sin = Opposite / Hypotenuse

Tan = Opposite / Adjacent

So, from the figure

Sin y = RS / AS Tan x = RB / RS

Since ∆ ARS and ∆ ABC are similar @ 90°

AR / AB = RS / BC

AR /18 = 5 / 7.5

From the given

AB = 18, RS = 5, BC = 7cm

AR = 5 / 7.5 × 18

AR = 12 cm

Now ∆ ABC, Applying Pythagorean theorem

AC² = AB² + BC²

AC² = 18² + 7.5²

AC² = 324 + 56.25

AC² = 380.25

AC² = 19.5 cm

In ∆ ABC

Sin y = BC / AC = 7.5 / 19.5

Sin y = 5 / 13

In ∆ ARS

Sin y = RS / AS

We know Sin y = 5 / 13

5 / 13 = RS / AS

5 / 13 = 5 / AS

AS = 13 cm

To Find Tan x

Tan x = RB / RS

In ∆ ARS

AS² = AR² + RS²

(13) ² = AR² + 5²

AR² = 169 - 25

AR² = 144

AR = 12 cm

Now RB = AB - AR

RB = 18 - 12

RB = 6

So, Tan x = 6 / 5

So the value of Sin y = 5 / 13

So the value of Sin y = 5 / 13 And value of Tan x = 6 / 5