In ABC, C 90, AB 13, BC 5, then how much AC on the other side, how much is the area, and what is the

According to the Pythagorean theorem: ab 2 = bc 2 + ac 2 gives 13 2 = 5 2 + ac 2 solution gives ac = 12

According to the area of the triangle equal to one-half base multiplied by the height, the area of abc is obtained abc=(1 2)*bc*ac=(1 2)*12*5=30

Height on hypotenuse = s abc (1 2) * ab = 30 (1 2) * 13 = 60 13

ac=12 Area=5*12=60 Height on hypotenuse=area ab=60 13

Using the Pythagorean theorem, the square of ac is equal to the square of ab minus the square of bc, and we can find that ac is 12, the area is the product of the two right-angled sides ac and bc, which is 60, and the height on the hypotenuse is the area divided by the hypotenuse as 60 13

Solution: From the Pythagorean theorem a 2 + b 2 = c 2 then ac=12. So s abc=1 2xacxbc=30 The height of the hypotenuse is 60 13

In fact, this problem is mainly about understanding theorems and formulas, and everything is solved!!

3. The triangle with the smallest overall area is a right-angled triangle with a high right-angled side. See image above.

bc=4/tan30º=4/(1/√3)=4√3sabcmin= bc*ac/2=4*4√3/2=8√3

Solution: In ABC, h=4

Bottom length = 4xcos30° = 4x 3 2 = 2 3s = 1 2x2 3x4

4 3 (square units).

A: The area of ABC is 4 3 square units.

Solution: In RT ACB, c=90

According to the Pythagorean theorem, there is ac=root(13-5)=12, and the area is 1, 2*5*12=30

Area = 1 2 * 13 * height of hypotenuse = 30

High 60 13 on hypotenuse

Pythagorean theorem.

ab^2=bc^2+ac^2

13*13=5*5+ac^2

ac=12 area is 5*12 2=30

Height on hypotenuse = 30 * 2 13 = 60 13

Solution: ab ac

The triangle ABC is an isosceles triangle.

bac＝120° ad⊥bc

cad＝60° ∠adc＝90°

acd＝180°-90°-60°＝30°∵cd＝6

Tan30° ad cd, ie.

ad＝tan30°×6＝√3×6＝6√3

s＝（6×2×6√3）/2＝36√3

Using the sine theorem to find the size of ab, according to the area formula s=, I calculate s=(75-25 root 3) 4