Question

if the right triangle ABC, angle C=90⁰, angle B=30⁰and AB =10 cm , find AC,BC and angle A​

Answer 1

Answer:

∴  ∠A = 60⁰ , AC = 5 cm  and BC = 8.66 cm

Step-by-step explanation:

Given,

In right triangle ABC:

∠C = 90⁰

∠B = 30⁰

AB = 10 cm

We know that

   ∠A + ∠B + ∠C = 180⁰      ( Sum of all angle of triangle is 180⁰ )

⇒ ∠A + 30⁰ + 90⁰ = 180⁰

⇒ ∠A + 120⁰ = 180⁰

⇒ ∠A = 180⁰ -  120⁰

∴  ∠A = 60⁰

    Sin B = $\frac{AC}{AB}$

⇒ Sin 30⁰ = $\frac{AC}{10}$

⇒ AC = 10 × Sin 30⁰

∴ AC = 5 cm

   Sin A = $\frac{BC}{AB}$

⇒ Sin 60⁰ = $\frac{BC}{10}$

⇒ BC = 10 × Sin 60⁰

∴ BC = 8.66 cm