in triangle ABC, angle ABC = 90, angle CAB = x, tan x= 3/4 and BC= 15 cm. find the measures of AB and AC
Answers
Given :- (Refer to image also.)
- in triangle ABC,
- ∠ABC = 90,
- ∠CAB = x,
- tan x = 3/4.
- BC = 15 cm.
To Find :-
- AB and AC = ?
Solution :-
since ∠ABC is equal to 90° . So, ∆ABC is a right angle ∆ .
in right ∆ABC now, given that,
→ ∠CAB = x,
→ tan x = 3/4.
→ BC = 15 cm.
So,
→ tan x = (Perpendicular / Base)
→ tan x = BC / AB
→ (3/4) = 15 / AB
→ 3AB = 15 * 4
→ 3AB = 60
dividing both sides by 3,
→ AB = 20 cm.
Therefore,
→ AB² + BC² = AC² (Pythagoras theorem.)
→ (20)² + (15)² = AC²
→ AC² = 400 + 225
→ AC² = 625
→ AC² = (25)²
→ AC = 25 cm.
Hence, Measures of AB and AC is 20 cm and 25 cm respectively.
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Answer:
Go through the attachment for reference
