Aright triangle has one angle that measure 23o. the adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.

what is the approximate area of the triangle? round to the nearest tenth.

area of a triangle = bh

Area of the triangle will be 161.70 cm²

Step-by-step explanation:

In the figure attached, in ΔABC  

m∠ABC = 23°

Adjacent side BC = 27.6 cm

and hypotenuse AC = 30 cm

Area of the triangle ABC =

=

By the sine rule,

sin23° =

AB = AC(sin23°)

     = 30sin23°

     = 30×(0.3907)

     = 11.72 cm

Area of the triangle ABC =

= 11.72×13.8

= 161.736 cm²

≈ 161.7 cm²

Therefore, area of the triangle will be 161.70 cm².

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

center= (-2,0)

radius= sqrt2/2

step-by-step explanation: