Answer:
The simplest right triangle is a 3-4-5 triangle which happens to add to 12.
So tangent of 4/3 = 1.33 or theta = 53.06 deg.
Also sin 4/5 = .8 and theta = 53.1 deg.
The other acute angle must be 180 - 90 - 53.5 = 36.5 deg.
Also tan 3/4 = .75 or theta = 36.9 deg for the other angle.
Step-by-step explanation:
Answer:
Angles of the triangle are 90°, 50.77° and 39.23°.
Step-by-step explanation:
Let the smallest side be x. Given that other sides are consecutive integers. So other sides are x+1 and x+2.
We have perimeter = 12 feet
So, x + x + 1 + x + 2 = 12
3x + 3 = 12
x = 3 feet
So the sides of the triangle are 3, 4 and 5 feet.
We have cosine formula
cosC [tex]=\sqrt{\frac{a^2+b^2-c^2}{2ab}}[/tex]
Consider a = 3 , b = 4 and c = 5
cosC[tex]=\sqrt{\frac{3^2+4^2-5^2}{2*3*4}}=0[/tex]
∠C = 90°
Similarly
cosB[tex]=\sqrt{\frac{3^2+5^2-4^2}{2*3*5}}=0.775[/tex]
∠B = 39.23°
∠A = 180-(90+39.23) = 50.77°
Angles of the triangle are 90°, 50.77° and 39.23°.
