randRange(5, 12) randRange(5, 12) randRange(20, 140) HYPOT * cos(ANGLE * PI / 180) HYPOT * sin(ANGLE * PI / 180) roundTo(1, 0.5 * BASE * HYPOT * sin(ANGLE * PI / 180)) $._("base") $._("height")

Find the area of the triangle.

Round to the nearest tenth.

var minX = min(0, APEX_X) - 1; var maxX = max(BASE, APEX_X) + 1; var scale = floor(min(400 / (maxX - minX), 300 / APEX_Y)); init({ range: [[minX, maxX], [-1, APEX_Y + 0.5]], scale: scale }); graph.baseLabel = label([BASE / 2, 0], BASE, "below"); path([[BASE, 0], [0, 0], [APEX_X, APEX_Y], [BASE, 0]], { stroke: BLUE }); if (ANGLE > 90) { graph.hypotPos = "below left"; label([0.6, 0], ANGLE + "^\\circ", "above"); } else { graph.hypotPos = "above left"; label([0.6 / tan(ANGLE * PI / 180), 0.4], ANGLE + "^\\circ", "right"); } graph.hypotLabel = label([APEX_X / 2, APEX_Y / 2], HYPOT, graph.hypotPos);
SOLUTION

The area of a triangle is `\dfrac{1}{2} \times \purple{\text{BASE_WORD}} \times \green{\text{HEIGHT_WORD}}`.

graph.baseLabel.remove(); graph.hypotLabel.remove(); label([BASE / 2, 0], "\\purple{" + BASE + "}", "below"); label([APEX_X / 2, APEX_Y / 2], "\\pink{" + HYPOT + "}", graph.hypotPos);

What is the height of this triangle?

var d = 0.4; if (ANGLE > 90) { path([[0, 0], [APEX_X, 0]], { stroke: BLACK, 'stroke-width': 1 }); path([[APEX_X, d], [APEX_X + d, d],[APEX_X + d, 0]], { stroke: BLACK, 'stroke-width': 1 }); label([APEX_X, APEX_Y / 2], "\\green{h}", "left"); } else { label([APEX_X, APEX_Y / 2], "\\green{h}", "right"); if (APEX_X > BASE / 2) { path([[APEX_X, d], [APEX_X - d, d],[APEX_X - d, 0]], { stroke: BLACK, 'stroke-width': 1 }); } else { path([[APEX_X, d], [APEX_X + d, d],[APEX_X + d, 0]], { stroke: BLACK, 'stroke-width': 1 }); } } path([[APEX_X, 0], [APEX_X, APEX_Y]], { stroke: GREEN });

`\green{h} = \pink{HYPOT} \times \sin(ANGLE^\circ)`

Therefore, the area of the triangle is `\dfrac{1}{2} \times \purple{BASE} \times \pink{HYPOT} \times \sin(ANGLE^\circ)`.

`\qquad \approx fractionReduce(BASE * HYPOT, 2) \times roundTo(3, sin(ANGLE * PI / 180))`

`\qquad \approx SOLUTION`

randRange(5, 12) randRange(5, 12) randRange(20, 140) HYPOT * cos(ANGLE * PI / 180) HYPOT * sin(ANGLE * PI / 180) round(sqrt((APEX_X - BASE) * (APEX_X - BASE) + APEX_Y * APEX_Y)) $._("base") $._("height")

Write an expression for the area of the triangle.

Round to the nearest tenth.

var minX = min(0, APEX_X) - 1; var maxX = max(BASE, APEX_X) + 1; var scale = floor(min(400 / (maxX - minX), 300 / APEX_Y)); init({ range: [[minX, maxX], [-1, APEX_Y + 0.5]], scale: scale }); graph.baseLabel = label([BASE / 2, 0], BASE, "below"); path([[BASE, 0], [0, 0], [APEX_X, APEX_Y], [BASE, 0]], { stroke: BLUE }); if (ANGLE > 90) { graph.hypotPos = "below left"; label([0.6, 0], "x", "above"); } else { graph.hypotPos = "above left"; label([0.6 / tan(ANGLE * PI / 180), 0.4], "x", "right"); } if (APEX_X > BASE) { graph.otherPos = "below right"; } else { graph.otherPos = "above right"; } graph.hypotLabel = label([APEX_X / 2, APEX_Y / 2], HYPOT, graph.hypotPos); graph.otherLabel = label([(APEX_X + BASE) / 2, APEX_Y / 2], OTHER_SIDE, graph.otherPos);

1/2 * BASE * HYPOT * sin(x)

The area of a triangle is `\dfrac{1}{2} \times \purple{\text{BASE_WORD}} \times \green{\text{HEIGHT_WORD}}`.

graph.baseLabel.remove(); graph.hypotLabel.remove(); label([BASE / 2, 0], "\\purple{" + BASE + "}", "below"); label([APEX_X / 2, APEX_Y / 2], "\\pink{" + HYPOT + "}", graph.hypotPos);

What is the height of this triangle?

var d = 0.4; if (ANGLE > 90) { path([[0, 0], [APEX_X, 0]], { stroke: BLACK, 'stroke-width': 1 }); path([[APEX_X, d], [APEX_X + d, d],[APEX_X + d, 0]], { stroke: BLACK, 'stroke-width': 1 }); label([APEX_X, APEX_Y / 2], "\\green{h}", "left"); } else { label([APEX_X, APEX_Y / 2], "\\green{h}", "right"); if (APEX_X > BASE / 2) { path([[APEX_X, d], [APEX_X - d, d],[APEX_X - d, 0]], { stroke: BLACK, 'stroke-width': 1 }); } else { path([[APEX_X, d], [APEX_X + d, d],[APEX_X + d, 0]], { stroke: BLACK, 'stroke-width': 1 }); } } path([[APEX_X, 0], [APEX_X, APEX_Y]], { stroke: GREEN });

`\green{h} = \pink{HYPOT} \times \sin(x)`

Therefore, the area of the triangle is `\dfrac{1}{2} \times \purple{BASE} \times \pink{HYPOT} \times \sin(x)`.

More simply we can write, `fractionReduce(BASE * HYPOT, 2) \sin(x)`.