To find the measure of side a, we can use the Law of Sines:
a/sin A = c/sin C
Since c is the hypotenuse (opposite the right angle), we know that c = a. Thus:
a/sin A = a/sin 90°
Since sin 90° = 1, the equation becomes:
a/sin A = a/1
Cross-multiplying, we get:
a*1 = a*sin A
Simplifying, we have:
a = a*sin A
Using the given values:
A = 60° 25'
Converting A to decimal degrees:
A = 60 + (25/60) = 60.4167°
Substituting A into the equation:
a = a*sin(60.4167°)
Since a is on both sides of the equation, we can divide both sides by a:
1 = sin(60.4167°)
To find the value of sin(60.4167°), we can use a calculator. The sine function gives us:
sin(60.4167°) ≈ 0.88318
Now, substituting this value back into the equation:
1 = 0.88318
Since 1 is not equal to 0.88318, the equation is not true for any value of a. Therefore, there is no solution for side a.
Determine the measure of side a ( to the nearest degree and minute).
cos a = cos A/ sin B
C = 90°
B = 143° 44'
A = 60° 25'
1 answer
1 answer