Question

How do you solve the right triangle given a = 84cm, A=35 degrees?

Answer 1

side `c=146.4495308" "`centimeters
side `b=119.9644326" "`centimeters
Angle `B=55^@`
Area `=5038.506169" "`square cm
Perimeter`=350.4139634" "`centimeters

Explanation:

From the given data:
Angle `C=90^@`
Angle `A=35^@`
side `a=84" "`cm

To solve for Angle B:

`B=90^@-A=90^@-35^@=55^@`

To solve for side `c`

`sin A=a/c`

`c=a/sin A=84/(sin 35^@)=146.4495308" "`cm

To solve for side `b`

`tan A=a/b`

`b=a/tan A=84/(tan 35^@)=119.9644326" "`cm

To solve for the Area:

Area`=1/2*b*a=1/2*119.9644326*84=5038.506169" "`square cm

To solve for the Perimeter P:

`P=a+b+c=84+119.9644326+146.4495308`
`P=350.4139634" "`cm

God bless....I hope the explanation is useful.