Question

A right triangle has a 30° angle and the adjacent side to

the angle of length 6, draw the triangle and label all
sides and angles. Round to the nearest tenth.

Answer 1

let the triangle be supposed ABC

where angle BAC is 30 degree and angle ACB is 60 degree and where we know that angle ABC is right angled triangle which means angle ABC = 90 degree

the base side of triangle is 6cm which means ;

By taking angle A as reference angle

Hypotenuse = AC = x(let)

perpendicular = BC

base = AB = 6 cm

then by taking base and hypotenuse

b/h = AB/AC

or, cos (30 degree)= 6/ x

x =
`4√(x) 3` cm

that concluded that AC =
`4√(3)` cm

Now,

by phythagorous theorem,

`h^(2) = p^(2) + b^(2)`

`AC =\sqrt{AB^(2) + BC^(2) } AC = \sqrt{6^(2) + 4√(3) ^(2)} \\AC = 2√(21 ) cm`

so, the length of side AB is 6 cm , BC is 4
`√(3)` cm and AC is 2
`√(21)` cm

Explanation: