In triangle ABC ; ∠ ABC = 90 ° , ∠ CAB = x ° , tan x ° = 3 4 and tan x ° = 3 4 and B C = 15 cm . Find the measures of A B and A C .

Consider the figure tan x ° = 3 4 ⇒ tan x ° = perpendicular base = B C A B = 3 4 Therefore if length of base = 4 x , length of perpendicular = 3 x Since, B C 2 + A B 2 = A C 2 [Using Pythagoras Theorem] ( 3 x ) 2 + ( 4 x ) 2 = A C 2 A C 2 = 9 x 2 + 16 x 2 = 25 x 2 A C = 5 x Now, B C = 15 ⇒ 3 x = 15 ⇒ x = 5 Therefore, A B = 4 x = 4 × 5 = 20 cm And, A C = 5 x = 5 × 5 = 25 cm

In the given figure; B C = 15 cm and sin B = 4 5 . Calculate the measure of A B and A C .

Given sin B = 4 5 ⇒ sin B = perpendicular hypotenuse = A C A B = 4 5 Therefore if length of perpendicular = 4 x , length of hypotenuse = 5 x Since, B C 2 + A C 2 = A B 2 [Using Pythagoras Theorem] ( 5 x ) 2 - ( 4 x ) 2 = B C 2 B C 2 = 9 x 2 ∴ B C = 3 x Now, B C = 15 ⇒ 3 x = 15 ⇒ x = 5 A C = 4 x = 4 × 5 ⇒ A C = 20 cm And, A B = 5 x ⇒ A B = 5 × 5 ⇒ = 25 cm

E M B I B E

Concise Mathematics I.C.S.E - Class IX>Chapter 22 - Trigonometrical Ratios [Sine, Cosine, Tangent of an Angle and Their Reciprocals]>EXERCISE>Q 6

EASY

9th ICSE

IMPORTANT

Earn 100

In the figure given below, $A B C$ is an isosceles triangle with $B C = 8 cm$ and $A B = A C = 5 cm$ . Find: $\tan C - \cot B$ .

Important Questions on Trigonometrical Ratios [Sine, Cosine, Tangent of an Angle and Their Reciprocals]

EASY

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 22 - Trigonometrical Ratios [Sine, Cosine, Tangent of an Angle and Their Reciprocals]>EXERCISE>Q 7

In triangle $ABC; ∠ ABC = 90 °, ∠ CAB = x °, \tan x ° = \frac{3}{4}$ and $\tan x ° = \frac{3}{4}$ and $B C = 15 cm$ . Find the measures of $A B$ and $A C$ .