Let's begin with recalling the Law of Sines. If â–³ ABC has lengths of a, b, and c and angle measures of A, B, and C, then we can write that the ratios of the sine of an angle to the side opposite this angle are equal.
Now let's look at the given picture. We will name the missing side lengths and angle measure.
The third angle in this triangle has a measure of 86^(∘).
To find the other two side lengths, we will use the Law of Sines. Let's write a proportion.
sin 43^(∘)/y=sin 51^(∘)/103=sin 86^(∘)/z
Let's start with evaluating the value of y using cross multiplication.
Now we can evaluate the perimeter of the triangle by adding all the side lengths. Remember that this will be an approximation as we are using approximate side lengths.
103+ 90.4+ 132.2=325.6
The perimeter is approximately 325.6 units.
