What is the value of x? show all of your work.

x = 9 cm

Step-by-step explanation:

The value of 'x' can be found using the Pythagorean Theorem.  This theorem applies to right triangles and uses the formula:

a² + b² = c², where 'a' and 'b' represent the legs of the triangle and 'c' represents the hypotenuse (diagonal)

Given the values from the triangle:

x² + 6² = (√117)²  or x² + 36 = 117

Subtract 36 from both sides:  x² + 36 - 36 = 117 - 36 or x² = 81

Take the square root:  √x² = √81

x = 9 cm

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

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step-by-step explanation:

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