In the right ∆ABC, BL is an angle bisector. If LB = 1.2 in and LC = 0.6 in. Find the distance from L to AB
AND find the measurement of

= 0.6 inch

m∠ABC = 60°

Step-by-step explanation:

The given parameters are;

The given triangle ΔABC = A right triangle

The angle bisector of ∠CBA = BL

The length of BL = LB = 1.2 in.

The length of LC = 0.6 in.

We have;

≅ reflexive property

∠ABC = ∠CBL + ∠DBL and ∠CBL ≅ ∠DBL definition of bisected angle

∠CBL = ∠DBL by definition of congruency

∠CLB + ∠CBL = ∠CLB + ∠DBL = 90°, opposite angles of a the right angle triangle are supplementary

∴ ∠CLB = ∠CLB by addition property of equality

ΔLDB ≅ ΔLBC are congruent by the Angle-Side-Angle rule of congruency

∴ ≅ Congruent Parts of Congruent Triangles are Congruent (CPCTC)

= = 0.6 in. by definition of congruency

= 0.6 in.

sin(m∠CBL) = Opposite side/(Hypotenuse side) = / = 0.6/1.6 = 1/2

m∠CBL = sin⁻¹(1/2) = 30°

m∠CBL = m∠DBL = 30°

m∠ABC = m∠CBL + m∠DBL = 30° + 30° = 60°

m∠ABC = 60°

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

answer: 94

step-by-step explanation: 79+91+92+94+94 = 450 divided by 5 (since there are 5 number that are being added) = 90