Question

0.7 In a right angled triangle, the acute angles
are in the ratio 4:5. Find the angles of
the triangle in degree and radian.
Q.8 The sum of two angles is 51° and their
difference is 60°. Find their measures in
degree.
Q.9
The measures of the angles of a triangle
are in the ratio 3:7:8. Find their measures
in degree and radian.
8​

Answer 1

Answer:

Explanation:

0.7 In a right angled triangle, the acute angles  are in the ratio 4:5. Find the angles of  the triangle in degree and radian.

Answer :-

Sum of acute angles (a+b) = 90

Ratio of acute angle , a/b = 4/5

Solving both we get, a = 40°, b = 50° ( a = 0.69 rad, b = 0.87 rad)

Q.8 The sum of two angles is 51° and their  difference is 60°. Find their measures in  degree. Mistake in question - Sum is 60°, Diff is 51°

Answer :- a - b = 51, a + b = 60

Adding both, 2a = 111

a = 55.5°

b = 4.5°

Q.9

The measures of the angles of a triangle  are in the ratio 3:7:8. Find their measures  in degree and radian.

Answer :-

Let a,b,c be angle of triange

a + b + c = 180°

3x + 7x + 8x = 180°

x = 10

So, the angles are 30°, 70° & 80°. (0.52 rad, 1.22 rad, 1.39 rad respectively)

Degress x Pi/180 = Radians.

Answer 2

Answer:

0.7

$50^{\circ},40^{\circ}$

$\frac{2}{9}\pi radian,\frac{5\pi}{18} radian$

0.8 $a=55.5^{\circ}$

$b=4.5^{\circ}$

$c=120^{\circ}$

0.9 $x=30^{\circ}$

y=$70^{\circ}$

z=$80^{\circ}$

$x=\frac{\pi}{6} radian$

y=$\frac{7\pi}{18}radian$

z=$\frac{4\pi}{9}radian$

Explanation:

0.7 We are given that a right angles triangle ,acute angles are in the ratio 4:5

We have to find the angle of triangle in degrees and radian

Let x and y be two acute angles of triangle

$\frac{x}{y}=\frac{4}{5}$

$x=\frac{4}{5}y$

We know that sum of angles of triangle =180 degrees

$x+y+90=180^{\circ}$ because one angle of a triangle is 90 degrees

Substitute the value of x then we get

$\frac{4}{5}y+y=180-90=90$

$\frac{4y+5y}{5}=90$

$\frac{9}{5}y=90$

$y=90\times \frac{5}{9}=50^{\circ}$

$x=\frac{4}{5}\times 50=40^{\circ}$

Using formula

Radian measure =$\frac{\pi}{180}\times$ degree measure

x in radian=$\frac{\pi}{180}\times 40=\frac{2}{9}\pi$

y in radian=$\frac{\pi}{180}\times 50=\frac{5\pi}{18}$

0.8 Let a,b and c are the angles of a triangle

According to question

if we take a+b=51 and a-b=60 then that case is not possible

So , it is a mistake in question

So , correction is

$a-b=51$

$a+b=60$

Adding two equation then we get $2a=111$

$a=\frac{111}{2}=55.5^{\circ}$

Substitute the value of a in equation first

Then we get $55.5+b=60$

$b=60-55.5=4.5^{\circ}$

Sum of angles in a triangle =180 degrees

$4.5+55.5+c=180$

$60+c=180$

$c=180-60=120^{\circ}$

0.9 We are given that the angles of a triangle are in the ratio 3:7:8

We have to find the measures of triangle in degree and radian

Let x,y and z be the angles of a triangle

Let a be the common quantity that multiplied with each value of ratio then we get all values of a triangle

Then x=3a,y=7a and z=8a

Then $x+y+z=180^{\circ}$

$3a+7a+8a=180$

$18a=180$

$a=\frac{180}{18}=10$

Then angle x=$3\times 10=30^{\circ}$

y=$7\times 10=70^{\circ}$

z=$8\times 10=80^{\circ}$

Angle x in radian=$\frac{\pi}{180}\times 30=\frac{\pi}{6}radian$

Angle y in radian =$\frac{\pi}{180}\times 70=\frac{7\pi}{18}radian$

Angle z in radian =$\frac{\pi}{180}\times 80=\frac{4\pi}{9} radian$