Question

If in the traingal ABC , AB:BC:CA=3:4:5 then find the value of the following:
a) sinA
b) cosA
c) tan C+secC
​

Answer 1

Answer:

• a) sin A = 4/5
• b) cos A = 3/5
• c) tan C+ sec C = 2

Step-by-step explanation:

Given:

• If in the traingal ABC, AB:BC:CA = 3:4:5

To find:

The value of the following:

• a) sin A = 4/5
• b) cos A = 3/5
• c) tan C + sec C = 2

Solution:

In ∆ABC,

We know that AB:BC:CA = 3:4:5

So, let AB be 3x, BC be 4x and CA be 5x respectively.

First we will prove that the given triangle is right angled triangle.

Refer the attachment...

So, we can use different trigonometric ratios to find the given respectively.

a.)

• sin A = P/H
• sin A = AB/AC
• sin A = 4/5

b.)

• cos A = B/H
• sin A = AB/AC
• cos A = 3/5

c.)

• tan C = P/B
• tan C = AB/BC
• tan C = 3/4

• sec C = H/B
• sec C = AC/BC
• sec C = 5/4

• tan C + sec C = 3/4 + 5/4
• tan C + sec C = (3 + 5)/4
• tan C + sec C = 8/4
• tan C + sec C = 2

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