Question

In triangle ABC, Angle C is a right angle. Find the value of the trig function. Find the Tan A if c=7√10 and a=21

Answer 1

tan(A) = 3

Explanation:

We know the following about triangle ABC:

• Angle C is a right angle
• Hypotenuse = c = AB =
  `7 √(10)`
• Opposite= a = BC = 21

We want to find tan(A).

The formula for tan(A) is:

`\sf tan(A) = (Opposite)/(Adjacent)`

In triangle ABC, the opposite to angle A is BC = a and the adjacent angle A is AC = b.

We can find b by using Pythagorean theorem which is:

Hypotenuse² = Adjacent² + Opposite²

c² = b² + a²

c² - a² = b²

`b =√( c^2 - a^2 )`

Substitute the given value:

`b =\sqrt{(7 √(10)) ^2 - 21^2 }`

`b =√((490- 441)`

`b =√((49)`

b = 7

Since we have:

`\sf tan(A) = (Opposite)/(Adjacent)`

Substitute the known value:

`\sf tan(A) = ( 21)/(7)`

tan(A) = 3

Therefore, the value of tan(A) is 3.