Question

ABC with C=90degree. solve for all the missing parts using the given info; A=12degree 42', b=6.832cm
B=______ ______
a=
c=

Answer 1

Answer on question 35931 – Math – Trigonometry

ABC with $C = 90$ degree. solve for all the missing parts using the given info; $A = 12$ degree $42'$ , $b = 6.832$ cm

B=

a=

c=

Solution

As we know the sum of acute angles of the right triangle is $90{}^{\circ}$ . Therefore,

Angle $B = 90{}^{\circ} - 12{}^{\circ}42^{\prime} = 77{}^{\circ}18^{\prime}$

From the definition of tangent we have

$$\tan A = \frac {a}{b}$$

From this equality we get

$$a = b \tan A = 6. 8 3 2 * \tan 1 2 {}^ {\circ} 4 2 ^ {\prime} \approx 0. 2 2 5.$$

Using Pythagorean Theorem we obtain

$$c = \sqrt {a ^ {2} + b ^ {2}} = \sqrt {6 . 8 3 2 ^ {2} + 0 . 2 2 5 ^ {2}} \approx 6. 8 3 6.$$

Answer: $\mathrm{B} = {77}{}^{ \circ }{18}^{\prime }$

a=0.225 cm

c=6.836 cm