Answer:
Step-by-step explanation:
It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...
AC^2 = AB^2 + CB^2
AC^2 = 4^2 + 3^2 = 16 + 9 = 25
AC = √25 = 5
The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...
scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8
And the scale factor to ∆BHC is ...
scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6
Then the side AH is 0.8·AB = 0.8·4 = 3.2
And the side CH is 0.6·BC = 0.6·3 = 1.8
These two side lengths should add to the length AC = 5, and they do.
The remaining side BH can be found from either scale factor:
BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4
_____
The sides of interest are ...
AH = 3.2
CH = 1.8
BH = 2.4
Answer:
20 degrees
Step-by-step explanation:
First, draw the triangle and label the sides and angles. (See the picture attached)
The red lines on sides FG and HF indicate that the sides are congruent since this is an isosceles triangle. Isosceles triangles have two congruent sides and angles.
All angles add up to 180 degrees. You were already given 140 for angle F. So, use to find angle h, subtract 140 from 180 and divide by 2.
180 - 140 = 40
40 / 2 = 20
Angle h is 20 degrees
