Answer:
Measure of EF: 1.98
Measure of AB: 6.16
Measure of HI: 12.2
Explanation:
Trick I learned that's very helpful when solving these problems: SOH (Sine, Opposite, Hypotenuse)- CAH (Cosine, Adjacent, Hypotenuse)- TOA (Tangent, Opposite, Adjacent)
MEASURE OF EF
you're starting with angle D which is 26 degrees. You have the measure of the Hypotenuse (DF) and you're trying to find the measure of EF (the segment opposite the angle) so you would use Sine
to do the equation, i'm going to use x in place of EF. 0.44 = sin(26)
Formula: sin(angle) = (opposite)/(hypotenuse)
Equation:
0.44 = x/4.5 <----------- multiply by 4.5 to get x by itself
4.5*0.44 = x <---------- 4.5 times 0.44
1.98= x <----------------answer
MEASURE OF AB
trying to find hypotenuse and you already have the adjacent angle so you would use cosine. Using y in place of AB. 0.616 = sin(52)
cos(angle) = (adjacent)/(hypotenuse)
cos(52) = 10/y <------ divide by y
y*0.616 = 10 <------------ divide by 0.616
y = 10/0.616 <----------- next you'll divide 10 by 0.616
y = 6.16 <-----------answer
MEASURE OF HI
trying to find adjacent, already have opposite so you would use tangent. tan(42) = 0.90. using z in place of HI
tan(angle) = (opposite)/(adjacent)
tan(42) = 11/z <------------ multiply z on both sides
z*0.90 = 11 <--------- divide by 0.90 to get z by itself
z = 11/0.90 <-------- divide 11 by 0.90
z = 12.2