Home
Class 10
MATHS
In DeltaABC , ltB=90^(@),tan A=( 3)/(4)a...

`In `DeltaABC` , ltB=90^(@),tan A=( 3)/(4)`and length of BC =180 m, ten find the length of hypotenuse of `DeltaABC`.

Text Solution

Verified by Experts

We know that , tan `A=("perpendicular")/("base")=(BC)/(AB)=(3)/(4)`
So , let BC=3k and AB=4k
Form Pythagoras theorem,
` AC^(2)=AB^(2)+BC^(2)=(4k)^(2)+(3k)^(2)=25^(2)`
`:. AC=5k`
Now , since BC =180 cm (given)

`rArr 3k=180rArrk=60`
`:. AC=5k=5xx60=300`m
So , length of hypotenuse is 300m
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/exemplar|29 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8a|20 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11 B|10 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|8 Videos

Similar Questions

Explore conceptually related problems

Find the length of AB for the given DeltaABC .

In a DeltaABC , if B=90^(@) , then tan^(2).(A)/(2) =

If tan x^(@) = (5)/(12), tan y = (3)/(4) and AB = 48 m. Find the length of CD.

If tan x^@ = (5)/(12), tan y^(@) = (3)/(4) and AB = 48 m, find the length of CD.

Given below are the lengths of the legs of right DeltaABC . In each case find the length of the hypotenuse of DeltaABC . (i) a=27cm, b=36cm (ii) a=7cm, b=24cm (iii) a=9cm, b=40cm

In triangle ABC, angleB = 90^@ and tan A = 0.75 If AC = 30 cm, find the lengths of AB and BC.

Given below are the lengths of the legs of right DeltaABC . In each case find the length of hypotenuse of DeltaABC : (i) a=32cm, b=60cm (ii) a=28m, b=45m . (iii) a=32cm, b=24cm

In DeltaABC, angleB=90^(@), angleA=30^(@), b=20cm , find a and c.

In DeltaABC, C=90^(@), A=30^(@), b=6 , find the remaining elements of the triangle.

In DeltaABC,angleB=90^(@)and sin A= (4)/(5) , then find the values of all other trigonometric ratios for angleA .