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.

- m∠ABC

Distance of L from AB = 0.6 in.

m∠ABC = 60°

Step-by-step explanation:

Given:

LB = 1.2 in

LC = 0.6 in

We have to find the distance of point L to AB or length of LD.

From right triangle ΔBCL,

Sin(∠LBC) =

                 =

                 =

                 =

m∠LBC = 30° [Since ∠LBC is an acute angle]

Since, ∠LBC ≅ ∠LBA

m∠LBA = 30°

Now from right triangle ΔLDC,

sin(∠LBA) =

sin(30)° =

LD = 0.6

Therefore, Distance of point L from AB is 0.6 in.

m∠ABC = m∠ABL + m∠LBC

             = 30° + 30°

             = 60°

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3