Construct a triangle HLB with HL=6cm , HLB= 60° and LB= 8cm. Measure and state length HB

Answer 1

From angle LBH drop a vertical line down to LH as the base. It cuts LH into two parts, at a point we cquld call D, creating 2 right triangles, LBD and HDB. The base of the left right triangle LBD is 4 and the base of the right side right triangle HDB is 2

the height of both, BD, is the same, 4sqr3.

Now work with the right side right triangle, HDB. You have 2 of its sides. Use the Pythagorean Theorem. Square each side, sum them, then take the square root.

4sqr3 squared = 16x3 = 48

2 squared = 4

48+4=52

square root of 52 is 2sqr13 = about 2(3.6) = about 7.2

Answer 2

John M.'s answer is correct.

You could also you the law of cosines, if you have trig yet.

Answer 3

Need to draw a figure but alas we don't have that capability.

So draw a line from B perpendicular to HL which makes a 30/60/90 triangle. Then the height of that triangle = 4√3. The length of the other side of HL- 4 = 2. So you have 2 / 4√3 right triangle and HB = √ (2² + (4√3)² =

√52 = 2√13