The diagram shows a right-angled triangle. 17 cm
hcm
40°
What is the value of h?
Give your answer correct to 1 decimal place.

h = 20.3 cm

Step-by-step explanation:

Apply trigonometric ratio formula to find h.

Reference angle = 40°

Opposite side length = 17 cm

Adjacent side = h

Thus:

Tan (40) = 17/h

h × tan (40) = 17/h × h (multiplication property of equality)

h × tan(40) = 17

(h×tan(40)/tan(40) = 17/tan(40) (division property of equality)

h = 20.3 cm (1 decimal place)

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1