Hello from MrBillDoesMath!
Answer:
b = 28 degrees
Discussion:
In general,
sin (90 - @) = cos(@)
Set 90 [email protected] = 62 => @ = 28 so
sin (90-28) = sin(62) = cos(28) => b = 28
Thank you,
MrB
You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
_____
Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
_____
As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
The answer would be
m= -25
no solutions → C
The 2 given lines are parallel and never intersect thus no solution
