Given: ∆abc, ab = bc, bm = mc ac = 40, m∠bac = 42º find: am

The length of AM is 26.50 units.

Step-by-step explanation:

Given information:  AB = BC, BM = MC , AC = 40, ∠BAC = 42º.

Since two sides of triangle are equal, therefore the triangle ABC is an isosceles triangle.

The corresponding angles of congruents sides are always equal. So angle C is 42º.

According to the angle sum property the sum of interior angles is 180º.

Law of Sine

Therefore the length of AB and BC is 26.91.

Since M is midpoint of BC, so

Use Law of Cosine in triangle ABM to find the value of AM.

Therefore the length of AM is 26.50 units.

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh