Question

In a right-angled triangle, the length of a base is 4cm and its perpendicular is 3cm. Find:
a) length of the hypotenuse
b) tan θ
c) cos θ

Answer 1

Explanation:

As per the provided information in the given question, we have :

• In a right-angled triangle, the length of a base is 4cm and its perpendicular is 3cm.

We are asked to calculate,

• length of the hypotenuse
• Value of tan θ
• Value of cos θ

Finding the length of hypotenuse :

By using Pythagoras property,

⇒ H² = B² + P²

⇒ H² = (4 cm)² + (3 cm)²

⇒ H² = 16 cm² + 9 cm²

⇒ H² = 25 cm²

⇒ H = √(25 cm²)

⇒ H = 5 cm

∴ Length of hypotenuse is 5 cm.

Finding the value of tan θ :

As we know that,

$\longmapsto \rm { \tan \; \theta = \dfrac{Perpendicular}{Base} }$

$\longmapsto \bf { \tan \; \theta = \dfrac{3}{4} }$

∴ The value of tan θ is 3/4.

Finding the value of cos θ :

As we know that,

$\longmapsto \rm { \cos \; \theta = \dfrac{Base}{Hypotenuse} }$

$\longmapsto \bf { \cos \; \theta = \dfrac{4}{5} }$

∴ The value of cos θ is 4/5.

$\rule{200}2$

Know MoRe!

Important formulae :

● $\rm { \sin \; \theta = \dfrac{Perpendicular}{Hypotenuse} }$

● $\rm { \cos \; \theta = \dfrac{Base}{Hypotenuse} }$

● $\rm { \tan \; \theta = \dfrac{Perpendicular}{Base} }$

● $\rm { \csc \; \theta = \dfrac{Hypotenuse}{Perpendicular} }$

● $\rm { \sec \; \theta = \dfrac{Hypotenuse}{Base} }$

● $\rm { \cot \; \theta = \dfrac{Base}{Perpendicular} }$

Trigonometry Identities :

$\boxed{\begin{array}{cc} \underline{\bf {Important \; Trigonometric \; identities}} :- \\ \\ \: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1 \end{array}}$