What is the length of side AC of the triangle?

Mathematics

1 answer:

ryzh [129]3 years ago

3 0

Answer:

AC = 25 units

Step-by-step explanation:

Given ∠ A = ∠ C then the triangle is isosceles and BC = AB , that is

7x - 1 = 5x + 5 ( subtract 5x from both sides )

2x - 1 = 5 ( add 1 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Then

AC = 6x + 7 = 6(3) + 7 = 18 + 7 = 25 units

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n200080 [17]

Answer:

1) $m\angle x = 35^{\circ}$ , 2) $m\angle x = 60^{\circ}$ , 3) $m \angle x = 40^{\circ}$

Step-by-step explanation:

1) Triangle is a right triangle since tangent line is perpendicular to the radius of the circle. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$ :

$m\angle x = 180^{\circ} - 90^{\circ} - 55^{\circ}$

$m\angle x = 35^{\circ}$

2) Both triangles are symmetrical right triangles since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$ :

$m \angle x = 180^{\circ} - 90^{\circ} - 30^{\circ}$

$m\angle x = 60^{\circ}$

3) The figure is formed by two symmetrical right triangles. These triangles are right-angled and symmetrical since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in quadrilaterals equals 360°, we find the value of the angle $x$ :

$m\angle x = 360^{\circ} - 180^{\circ} - 140^{\circ}$

$m \angle x = 40^{\circ}$

4 0

3 years ago

What is the surface area of the composite solid? a rectangular prism with a length of 2 meters, width of 8 meters, and height of

Anna007 [38]

Using the formula for the surface area of a rectangular prism, the surface area of the composite solid is: C. 162m²

<h3>What is the Surface Area of a Rectangular Prism?</h3>

Surface area of a rectangular prism = 2(wl+hl+hw)

Surface area of the composite shape = surface area of the larger prism + surface area of the smaller prism - area of the face both prisms are joined together

Surface area of the larger prism = 2(wl+hl+hw) = 2(2×3 + 9×3 + 9×2) = 102 m²

Surface area of the smaller prism = 2(wl+hl+hw) = 2(2×8 + 2×8 + 2×2) = 72 m²

Area of the face both prisms are joined together = 2(l×w) = 2(3 × 2) = 6 m²

Surface area of the composite shape = (102 + 72) - 12 = 162m²

Learn more about surface area of rectangular prism on:

brainly.com/question/1310421

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